What is the difference between a unit CPL and a DOD CPL?

A CPL is a CPL period, regardless what unit they are in.

You are either laterally appoint a CPL, or no, long gone are the two types .

Lateral promotions CPL are used to fill open NCO positions (must be an authorized position, the unit can not make one up..Like say, company training room clerk.. That is not an authorized position, it is not the SM PMOS, so as such it is not eligible for a SM to serve in it and be a CPL.

Even if your new unit has an NCO opening, in your PMOS, as your new to the unit and untested, they will likely laterally promote a SPC in the unit to CPL

The reg states "A SPC will be appointed to CPL when the Soldier is assigned and works in a SGT position. The position must be the Soldier’s PMOS or CPMOS. "

The second you sign over your unit property at the loosing unit, start your clearing process...you no longer meet the requirement for the lateral promotion. It would not be wrong for a loosing CMD to Revert the CPL to SPC before the PCS.

If a loosing unit does not do that, the gaining will in most all cases as the gaining is not likely assigning you an unfilled NCO position in your PMOS.
If they had such an opening, they are likely to laterally promote a SPC in the unit already.