Would it help to describe the way MIDI segregates Left and Right on my Yamaha Clavinova piano? There are a few options for single, dual, split and split+dual voices.
In its startup configuration, the keyboard creates a single MIDI track containing the notes played by both hands. I can assign that stream of MIDI events to a MIDI channel I choose. This is how I use MIDI presently to communicate with a software program I am writing.
The piano control panel has a Dual/Split button and a piano setting to set a keyboard split allowing two voices: one for keys below the split and another for keys above the split. The Piano's MIDI output configuration settings allow the user to map each voice to a distinct MIDI channel. (I have not checked whether the piano allows both voices to be assigned to the same MIDI channel - it would not make a lot of sense to do this if it was not possible to segregate the MIDI events into two voices - but you never know until you try!) I think the piano adjusts the Key number in the MIDI event so that both splits report notes either side of a middle C (note 60 in MIDI) as though you were playing two distinct keyboards.
The piano also has a feature allowing two voices to be generated at the same time for the same keys. In these configurations the keyboard generates duplicate MIDI events that can be assigned to two distinct MIDI channels.
Finally, there is a Split+Dual mode in which the Right hand split has a dual voice. This should allow a keystroke above the split to generate duplicate MIDI events - overall this would create events assignable to 3 MIDI channels (Yamaha use L+R1/R2 in their MIDI manual when describing this).
The Piano settings has a section devoted to configuring MIDI. The MIDI settings in the piano allow me to set the MIDI channels for each output (and each input if also sending MIDI events to the piano synthesiser or sequencer).