Wow! Seven years later and if I didn't know the difference between an audio file and a MIDI file, I wouldn't be able to get a job. Funny how time changes things.
Just to clarify: CinccinoFloof is pretty much right about MIDI versus audio files. They're files that give a computer instructions on what to perform, and then the computer will perform it; the audio is not recorded. This allows for multiple things, but perhaps most notably in this situation the capability to assign different instruments to a MIDI file, which means, for example, if I had a MIDI file of the best opening track ever, Highway Star from Deep Purple's 1972 masterpiece Machine Head, I could make any instrument I wanted play the guitar solo. Eat your heart out, Richie Blackmore, it's a trombone solo now. Obviously, you can't do this with an audio recording file (most commonly .mp3 or .wav but there are a whole load more), but you can record a MIDI file as a normal audio file. This is actually super common, virtual instruments (which interpret MIDI data) can be made to sound incredibly convincing (if you know how to do it).
Preamble and jokes over. I came across this question and wanted to answer it because I find the current answer unsatisfactory as there isn't really a citation beyond sumwun just asking the question on another forum (honestly, this question should have been on the unanswered list).
I went digging around and I think I can (perhaps through circumstantial evidence) confirm that, yes, MOST of the music in the games are performed by MIDI files or something similar used to sequence the music, rather than played back through audio files. Some evidence of this is from MIDI rips on musescore. While it's ENTIRELY possible that someone could just be incredible at transcribing, I doubt it. Check out this transcription of the Gamefreak Logo. I don't think anybody would take the time to transcribe this, as there's nothing very musical about it, though, if the "Midi rip" in the title wasn't enough to sell you, the rhythms here are ultra specific. The sorta weird crap you'd see in a transcription of a Van Halen solo, or perhaps as specific as a reference I make that nobody's gonna get. If you want another musical example, look no further than this rip of the Black and White title screen. Again, super specific. Would be incredibly hard to transcribe by ear. If you're curious about more the user that made these has an entire catalogue of rips.
Here's some more circumstantial evidence. I found this download link for MIDIs from B/W and B2/W2 (note that there's pretty much no reason to download this unless you like playing around with MIDIs. I'm not even sure if this website is trustworthy, as I am far too hasty when it comes to downloading things online). Upon inspection, this has most of the music featured in the games (I guess I'm assuming but I'm not going to cross-reference), though it's noticeably lacking the title theme for B2 and W2 (it does have a file that suggests that it's there, but it's not the same thing).
My third (and weakest) piece of evidence regarding this is simply the sound of the music. It's incredibly articulate, notes aren't weirdly cut off like music performed by MIDI often is. All this leads me to believe that, yes, the title screen is an audio recording, rather than sequenced music. It's worth noting that, as I mentioned earlier, MIDI can be made to sound incredibly convincing, though keep in mind that B2/W2 were released in 2012 and have, to my knowledge, much of the same soundfont as the originals, implying that the technology they were using for the music was no newer than 2010. On top of that, the title screen music has a considerably different sound than the rest of the music from the game, meaning that, were it MIDI, it'd have to be a different set of more convincing sounding virtual instruments, and it would be a strange choice not to have the rest of the game sound like that, as applying different sets of instruments to MIDI files is quite easy.
TL;DR: The evidence I've found points to the music for the title screen being recorded audio rather than MIDI, unlike the rest of the music in the game.
I wish I could give a definitive answer, but this is better than the old one, right? Hah.