"Instant Codes" is an option that became available after game developers started putting anti-piracy measures in their games. For example, when Chrono Trigger was released for the DS, it had a built-in anti-piracy check that would cause the game to freeze at a certain point early in the game if you were playing the ROM on a flashcart. Then a cheat code was created to bypass the anti-piracy check, and everyone was able to play the ROM without any freezing.
In the past, there were only three options: Off, Switch On and Always On. Whenever you use "Always On," there's a short delay from the time you load the ROM until the time the cheats are actually active (about 10 seconds). Game developers realized this, so they exploited this fact and started putting their anti-piracy checks at the very beginning of the game (e.g., during the title screen). So the anti-piracy measure would be activated before the cheat codes had a chance to turn on. This happened with Dragon Quest V. Even when an AP check bypass cheat code was created for the game, it didn't work because the AP check turned on before the code did.
Instant Codes solved that problem by activating cheat codes as soon as the ROM is loaded. Basically, "Always On" and "Instant Codes" are the same thing, except that the latter is activated instantly without the delay. You should just use "Instant Codes" all the time. I personally think "Always On" should be removed from the options and "Instant Codes" should replace it completely.