So, final(s) as in final decision to land - yes?
"Final" meaning that you are on the "final" leg of the circuit pattern, i.e. heading toward the runway with the intention of arriving on it. If the airfield has ATC this is usually where you'd get clearance to land.
"short final" is a subjective term to mean 'last bit of finals'
"long final" used to indicate to ATC/other traffic that you are approaching the airfield from a distance and planning on a straight in approach. In the UK (CAP413) this is 4nm to 8nm.