There are more than two categories here, though using yours as a framing
1) Stocks are sections of a company that get sold off at various points in time with various abilities attached to them. Sometimes this is rights to vote during the company meetings (though not all companies will do this, and some might even have different flavours of shares that allow more votes), sometimes this is a slice of the profits (something called dividends, not all companies do this though).
When a company gets big enough it might in turn be listed on a public stock exchange (there are many out there) in what is called an initial public offering aka IPO. These can see values fluctuate quite rapidly and gain (or lose) a lot of people a lot of money.
If a company is not on a public stock exchange it is called a private company. You can buy shares in such things (it is how various investment firms make money -- buy in for say $50000 when they are small and if the company later gets valued at 50 million you have probably made a lot of money. Tech companies are often this -- most will fail but trap enough groups of three or four coders in a room and eventually you will get a winner) but you will have to know someone with the shares or get them from the company themselves (maybe because you work for them even).
You can buy shares to sell them when they have risen in price as well as take a cut of the dividends. You can also do so called short selling wherein you basically make a bet that the stock will fall (say a game company, which only makes one game a year or two, has a stinker coming up because you saw early reviews/demos then prices will most likely go down*. Careful where you learn info though -- if you know a coder in the company and they say the next game is crap that might well be insider trading which is "very rich people go to big boy jail" levels of illegal) and then deliver it at a later date. This shorting lark is what various big funds were doing the other week to gamestop until some others realised that they had technically promised more stock than existed (not necessarily as bad as it sounds**) and thus if a few normal peeps all jumped in and bought it (holding onto it afterwards) then when it came time for the big funds to return the shares they borrowed for the short then they would have to pay any price (hedge funds might be big and powerful but they are as nothing compared to the force that gets brought to bear if you don't pay up).
*you also have the thing that most traders only care about the year end or even just next quarter. If say Rockstar only releases table tennis and a lame GTA DLC pack then price will likely go down as they won't make much, however if I realise GTA 6 is coming out next year I might want to buy low when that news hits and then keep it for a year and sell then when all the GTA 6 money is coming in aka "buy low, sell high". Many investors will also note the differences between such companies -- a company that releases two products a year is potentially going to make a lot but also lose a lot, whereas a company that only does something boring and basic like food might be reliable but not earn much nor be likely to lose much.
**if it is due at days 5, 10, 15 and 20 you can give it back at 5, buy it back again and give it at 10... Similar to how some people will buy 5 houses and have the rent from various others pay the mortgage on the others in a line and possibly have a job that pays for it when not being rented. At least until the plant in town closes down and everybody leaves.
Anyway you and I don't have millions to put down so we don't speak to stock exchanges directly and have to speak to a broker, or use a secondary service like spread betting (literally a betting service but they follow money markets rather than ponies or people throwing a ball around). There are many brokers that charge various fees for their services (annual, per transaction, percentage...), and some that charge none but are generally awful (see the Robin Hood** program that was in the news a lot lately, though it is not the only one).
There are also secondary schemes like index funds wherein you buy a portion of a fund that theoretically does nothing else than have multiple of every share on an exchange (when you see "day's trading ended at" then that is the price for one of each share on the exchange, some of them can be several hundred dollars or more for a single share, though again there are services that mirror that). On average the various stock markets go up quite a few percent year on year (plus dividends), likely considerably more than your bank is going to give you for savings or current account interest.
Index funds (and equivalents
https://www.marketwatch.com/investing/Fund/SPY ) are boring and basic and if you reckon you can buy all the good stuff and ignore the bad to make even more then you are playing trader. Know however that the fanciest of traders with the fanciest of computers, news sources, education, teams working for them... rarely beat the market for more than a few years in a row.
There is also high frequency trading, though that we can probably skip for now.
**choice video and will cover some other fun things
There are also things like Forex (foreign exchange). Here you convert money between different currencies and aim to make something from fluctuations in value (war was declared, price goes down, Olympics coming to town, price goes up as all those tourists, everybody wants the new device from this country then look out import prices...). There are platforms, and you can even do it down your local place you buy holiday money if you want (though prices are seldom that good compared to big money online options or those companies get to use -- compare
https://fxtop.com/en/currency-converter.php to your local supermarket if you want). That said very few people will seriously do this and make something. It is mentioned mostly so you can avoid them when you inevitably run into the adverts for it. If you are a big company doing importing and exporting of goods and materials you may have to deal with it, though US dollars often spend well wherever you are.
There are also tangible items you can invest in. Gold and silver for instance, oil is another. This is part of something called derivatives. The reason oil was so low last year was because you are duty bound to take delivery of it eventually. As everybody started sitting at home then there was an excess of it and guy sitting in wall street bank generally does not have an oil storage plant and thus was desperate to offload it before they had to take it or pay fines.
For precious metals you can buy them and have them sit somewhere, or you can buy them and keep them with you (and deal with having to store it) before fobbing them off to somewhere else or one of those cash for gold places if you like.
2) Cryptocurrency.
A different concept.
Such things are basically distributed ledgers that can be somewhat anonymous (it is possible to use them such that you are plain for all to see, though also not to).
You can get a "wallet" and purchase some crypto from someone (I have seen shops in malls, people on the street/internet, exchanges) or mine it (the distributed ledger is basically a computing problem so chuck enough computing power at it and you might gain some in exchange for the work, costs to do it are quite high so you are mostly hoping the conversion rate goes way up at this point).
You can also have an account on exchange (though a favourite phrase there is there are two types of crypto currency exchange -- those that have been hacked and those that don't yet know they have been hacked) which turns it into a lamer version of something like paypal, though sometimes more quick to access.
Anyway anonymous transactions for drugs, quick international transactions, transactions without much fees... all good stuff that people want to do. This means the price people will pay for a single unit of crypto potentially goes up and up, sometimes quite a lot (
https://www.coindesk.com/price/bitcoin . Buy into bitcoin when it was less than 1000 per coin in 2014 and sell today when it is north of $40000 and that is a large jump, buy in earlier still when it was still a few dollars or cents per coin and... yeah, way more than any stock trader or savings account interest. Though at the same time had you bought in during the peak of 2017 then you would only have late last year broken even).
Anybody can make a new cryptocurrency but the trick is getting people to use it.
For the most part there is bitcoin and all the rest, all the rest sometimes being referred to collectively as altcoins. Altcoins are also themselves about 5 anybody cares about (ethereum you might have heard of as it was partially responsible for driving graphics card prices up the other years) and all the rest.
You can also speculate on these on some of the spread betting and other applications mentioned in 1) (they also have sections for currency and such things are basically currency) without ever really owning any.
Anyway that is but the briefest of overviews (other than that video I did not even really cover many terms you might hear). Hopefully it is enough that you can search for more.
As a general rule never invest what you can't afford to lose. Spread your investments over various fields aka diversify your portfolio so one industry tanking (or part of a secondary industry related to it) does not wipe you out.
If it is for fun then that is one thing, if it is actually for a retirement plan or something then figure out what you will need and work accordingly -- you don't necessarily have to make all the money if you are on track to make enough and thus you might use some excess to do something a bit riskier. Your flag says US so probably also want to learn what a Roth IRA and 401K are, and actually do something with it (simply paying into a bank might do nothing much if you don't tell them to invest it, which is apparently a thing many have done). Do also pay attention when tax season comes around (can be good, can be bad, the government will come and get you if you screw up), and maybe learn about virtual losses too as the tax man generally cares about your profits rather than your income.
