Hi --
Welcome to the Forum!
I recommend studying the difference between MIDI tracks and MIDI channels. Then the difference in Standard MIDI File (SMF) type 0 and type 1 will make more sense.
"Track" is actually a Standard MIDI File concept/entity. You're right. Type 0 has only one track and Type 1 allows multiple tracks.
If I want to separate the right and left hand parts into two tracks, I would record the right hand into one SMF track and record the left hand into one SMF track. The SMF itself should be saved as Type 1 in order to preserve the track structure.
Now, what could be confusing. Each track typically has a MIDI channel assigned to it. Conventionally, track one gets MIDI channel 1 and track two gets MIDI channel 2. The same piano voice may be selected on channel 1 and channel 2 -- no biggie.
In MIDI SMF Type 0, all MIDI data is in one track. If the left hand part and right hand part are on MIDI channel 1, for example, then the left and right hand parts cannot be separated out. If left hand is recorded on channel one and right hand is recorded on channel two, then at least you have some chance of separating the two parts.
Hope this helps -- pj