MIDI
Recently (1 week ago?) I recorded something with the electrical piano in Rosegarden in MIDI (USB in between the device and the computer), out of curiosity (see whether or not that would work) I imported the MIDI to MuseScore. What I heard when I played it within Musescore was strongly different from what I heard when I played the to MP3/WAV converted MIDI-file with a music player. The MIDI-file was generated by Rosegarden based upon the input from the electrical piano. I used the latest version of Musescore which I downloaded via the software manager of Kubuntu. For whatever reason Musescore added a lot of notes and with a weird duration of the notes. Just pointing it out. You probably shouldn't input MIDI anyway unless you've got an incredibly tight rythm.
Comments
There are options useful when you import MIDI files into MuseScore. They will make the rhythms better, but as you suggested, they will not likely be perfect unless you have a very tight rhythm. The difference in sound is also largely based on the different sound fonts used for playback. You said your MP3/WAV used your keyboard font, while MuseScore uses a different one.
Indeed, MIDI doesn't record actual sounds, just timing instructions, so of course different programs will redner them differently, just as two different violin players will sound very different playing the same music. Howeve,r it shoudl still be the exact same notes in the exact same order for the exact same durations. Of course, it's perfectly normal that notes that aren't exactly a beat long (or whatever) may end up looking strange - notated with ties and so forth to give the original duration. That's normal and correct and should still sound the same (other than different instrument samples of course). You can always quantize in your MIDI software. Also see the options in the MIDI import panel within MuseScore.
If you have a MIDI file where you believe things are not happening as they should, please attach it so we can investigate.