One-fingered tap is the primary click, and two-fingered tap is the alternate click.
Holding the control and command keys while clicking (with one finger) can also bring up additional functions, depending on the context. Holding the control key while clicking with one finger is, well, control click.
My phrasing here? On a mouse, there’s a primary and a secondary or alternate click or control click, and mice do sometimes have a third button or yet additional buttons. Why primary and secondary or alternate? Because the leftmost and rightmost buttons switch in function, depending on whether the mouse is configured for left or right-handed operations. That is, “left” and “right” as mouse button labels gets ambiguous quickly.
Yes, most folks that are either left-handed or ambidextrous are used to the confused phrasing of right-handed users, too.
As for using the Apple trackpad, different Mac trackpads have different capabilities. Older tadkpads lacked various multi-touch gestures. Pretty much everything has primary and secondary click, though.
Here’s the current set of gestures for Apple trackpads: Use Multi-Touch gestures on your Mac - Apple Support