1:1 can mean different things to different people in different scenarios, and that might change with time.
Though examples are probably good.
I suppose we can skip going in depth about interleaving. We did however see some variations on this theme with those nice gigaleaks wherein Nintendo's ROM reference collection was different to what those in the rest of the world know.
Bad dumps. Dumping with some older setups was not a precise art that it might be today for some. To that end if a connection came loose in a nice home made dumper then a small run of data might have been different. When the SNES collection was redumped the other year a few were noted in this (a spiderman game being among those if memory serves), and it happened at various points throughout the lifetime of other newer devices as well (the DS had quite a few). Groups like no-intro seek to make as accurate collections as they can here.
I also suppose we can skip any user added data -- a ROM file might just be that, however an emulator/flash cart might really appreciate being told more data about the makeup of the original cart. There is a subtle variation of this on the DS. Here for ROMs prior to the DSi launch then there was a blank space in the header. After the DSi became a thing then this area was used to house some data on the ROM so that Nintendo could authenticate it in the DSi (and later 3ds). Earlier dumpers however did not care about this and continued to leave that blank. This is also why the Scene release list of DS games has a bunch of redumps late in the day, however the extra info if of no use to any flash cart user, ROM hacker, emulator author, fancy FPGA system recreator (unless they want to go 1:1 and include protections that nobody cares about), emulator player or game historian will likely ever care about. So not 1:1 and justifiably redumped in any Scene rule set (
https://scenerules.org/ ) or preservationist effort but nobody actually really cares, and indeed it is probably more annoying for people as different "versions" might make patching things harder in the case of ROM hacks.
The DSi also has a further twist in that it had a special DSi version of some games that had extra features for being on a DSi. However if presented to a DS (or something pretending to be one) it would present a cut down DS version of it. Dump that and you might well be able to play the DS version exactly as it was but it would not be 1:1 for the purposes of preservation, and those looking to use the DSi extras. Note other than nicer wireless there is no real benefit to being on the DSi for anything -- the DSi was a failure.
Encryption is a thing.
If you can't read the proper data then things can be protected from filthy pirates (usually for about 5 minutes but different discussion there), hackers and whatnot. Sometimes dumpers will skip encryption to make life easier for emulators/flash carts. This would fail to be 1:1 for some purposes but most won't care.
Padding is a thing.
Most discs and ROM chips have a fixed size. Games have no requirement to be that size however.
This extra data is data that is literally there on a cart/optical disc/whatever. Some will trim this, and if the data is not easily trimmed then might be trimmed further, or indeed even shrank down such that you need a completely hacked system to make use of it.
The Wii "scrubbing" methods featuring such a thing where any padding between files early on the disc was removed and files put end to end, different to baseline where just the padding was replaced with 00 and thus the iso would compress down nicely where before the random data made them hard to meaningfully compress. The Wii also featuring further things where isos were packed into all manner of weird and wonderful formats (
https://wit.wiimm.de/ ) for use with different loaders, and sometimes distribution. Today we have tools that can recreate lost data but for a hot moment...
The real fun.
Hacker and user added methods and dumping "failures".
Hacker and user added methods.
Three main forms.
1) To work on a given flash cart/emulator setup. Golden Sun Team on the DS probably being the most infamous here but there are others -- the 360 for instance often had data it needed to fake anti piracy checks buried in parts of the game not used and the (hacked) firmware on the DVD drive could use. Extras, encryption, anti piracy protection removal from code itself (might be a perk but not 1:1) all being things seen and sometimes necessary to do.
2) ROM ripping. Yes annoyingly it is the same term some quite rightly use as a synonym for dumping. Classically though a ROM rip saw parts of the game removed or decreased in quality to reduce space used (less storage, less bandwidth, more games on cart/disc/drive...).
Not so commonly seen nowadays but was seen on the DS in a few forms. Most were user derived affairs (I have a nice list of ones I made many years ago
https://ezflash.sosuke.com/viewtopic.php?t=457 ) but there were a few Scene groups that compressed the binary in the ROM (so not 1:1 and arguably even made things slower to load but smaller on the cart).
For the original xbox this was basically standard as well, mostly as single layer discs were cheap. Caused a lot of them to have to be redumped when the xbox 360 rolled around and did want those 1:1 or essentially so dumps to be played on that.
3) While bad dumping was covered earlier there is a subtle variation. For this we probably want to go to the original xbox. In it there was a 8 gig hard drive, and by the time the OS and whatever else was taken care of you were looking at 2 or 3 gigs available to play with. Dual layer DVDs were a thing by this point, indeed many games used them. If you ripped the files by alphabetical order you might find yourself changing the file order on the disc. Burn this back to a disc and those files carefully picked to be next to each other on the disc and take a fraction of a second less to get to now need a longer read and your game lags (assuming you were not running it from the hard drive which was faster than DVD anyway).
Trainers are also a thing. Here a group might patch a game to have a nice menu to make some cheats be in the game.
So yeah a brief overview of a few things. Chances are your 8-16 bit era games are good though, and most of the times any errors that made it through are a few pixels or something messed up for a random NPC nobody cares about -- errors in code tend to make things crash, and many times people have dumped their own versions over the years anyway.
Whether they are the same... well there are different versions to consider --
https://www.zeldadungeon.net/wiki/Ocarina_of_Time_Versions as well as regions (if you were used to playing PAL games then playing NTSC might be a rather different experience, and vice versa, and it is not always PAL being inferior slowdown and borders but maybe less censorship or bug fixes).
