I do not understand what your question is asking.
Let me step back a second for you. With a DAW, you can record audio/MIDI tracks into your computer, and then easily modify that data as you choose. A massive advantage of a DAW is that you have this information in a computer, and can apply effects, etc. without having to re-record it (time intensive), or lose sound quality as you "edit" effects and sounds. By keeping tracks separate (drums, vocals, synths, etc.), you can also choose how they are mixed for the final song. Then if you change your mind later, all of those tracks are still there and can be edited again in the future.
X3 includes a number of "soft synths" which basically "make the sounds" of MIDI notes being played (i.e. your Axiom AIR 61). A MIDI note
by itself is nothing more than which note you are playing, how loud you played it, when it started and stopped, and a few other things... but no "sound." With "soft synths," you can play a MIDI controller (keyboard), and hear the sound you choose (piano, synth, bass, drums, etc...). An advantage is you can record MIDI, assign it to an instrument (say an oboe), but then later on you prefer a saxophone... you can simply assign those same notes to a different instrument.
In all honesty, the "controller" aspect of a keyboard "driving" X3 is a nicety, but is not needed to record music. The "note data" is what X3 needs to make sounds, and you can record this easily with any MIDI input into X3. With those notes... X3 then makes the "sounds" you wish to hear (and you can tailor to your liking).
Did I answer your question at all, or just add more confusion to the fire?