BC***: Best case speed, i.e. high voltage, low temperature, fast nmos, fast pmos
NC***: Normal case speed, i.e. typical voltage, typical temperature, typical nmos, typical pmos
WC***: Worst case speed, i.e. low voltage, high temperature, slow nmos, slow pmos.
I'm not sure what LTCOM is.
I'm guessing the COM means commercial grade but it could mean something else depending on your vendor.
Typically when doing STA hold analysis BCS is assumed and when doing STA setup analysis WCS is assumed.
Simulations should be ran across all three corners: BCS, TYP and WCS.