This nomenclature comes, in CMOS processes, from the time where these were mainly used for digital circuits. The foundries make a characterization of their processes, analyzing the variations that it has. Then they build a model for the slowest, typical and fastest cases. If you compare these models almost all parameters have variations. One of the things that change and has a direct impact on the behavior of the transistors is the oxide thickness (tox).
TT, FF, SS, FS, SF corner cases take all process deviations into account.
The SPICE model parameters, are listed below, usually changed for corner analysis (for N- and P-MOST).
TOXM, DXL, DXW, DELVTO, CJ, CJSW, CJGATE, CGDO, CGSO.