The same concepts for music production apply to game music and sound effects. The tools vary, and are largely dependent on preference. All DAWs (digital audio workstation) do the same basic thing, record and mix sounds, and it boils down to the sound engineer’s preference. Like there are different kinds of cars but they get you from point A to B all the same.
MIDI, like the other comment explained in depth, is just a standard communication protocol. For example, when I use my MIDI controller keyboard, the DAW records my keystrokes (what note I pressed, how hard and how fast and how long I pressed it, and if I wiggled my finger). But my keyboard doesn’t produce sound, it just sends all the keystroke data to the DAW, and I can choose whatever sound I want it to make using virtual software instruments/soundfonts or plug-ins. Compare that to traditional recording where you play an instrument (i.e. guitar) and you literally just record the sound it produces.
When making game sound effects, you can either literally just produce those sounds and record them with a microphone into your DAW (more authentic), or use virtual sounds controlled by MIDI (more flexible and sometimes cheaper but might not sound realistic depending on your sound engineering skills).