Yeah, "trigger" refers to the letter buttons (several manuals and in a handful of cases the games themselves refer to "A trigger" / "B trigger" / "C trigger"). Contrast with Start button and Directional Pad.
B maps to the Atari button because the Master System controller has two buttons and their internal order is arranged left to right (1 and 2, respectively), and for whatever reason Sega wanted 1 to be the main button (it was even labelled "Start"). The Mega Drive controller is backwards compatible and they actually got the memo to be ergonomic this time, so 1 and 2 got mapped to B and C (while A is the "new" button, despite being the first letter-wise).
Backwards compatibility is awkward like that.
EDIT: more to the point
Then again, most games seem to use different controls for title screen and Options, and in many cases they didn't even provide a way to cancel. But this isn't the '90s anymore, give players some slack if they select the wrong option :v
Sik is pronounced as "seek", not as "sick".