SQL is a mix of SPL and SQ. It has popped up because of SPL competitions' focus on single frequency SPL. People want to explain that they want high SPL, but at the same time want to listen to music.
I typically define users into two orthogonal axii:
objective vs subjective
loud vs not loud (or not as loud as the equipment is capable of).
this gives 4 combinations:
SPL Competitor -- loud, objective (only measurements matter)
SQL/Street -- Loud, subjective (interested in high SPL, but also deep and clean sound)
HiFi -- not loud, objective (determines sound quality by extensive measurement)
SQ -- not loud, subjective (determines sound quality by experience and opinion)