amusing

Where it comes from

Amusing ordinarily means entertaining or funny. Amuse came from French amuser, formed from a- and muser, a verb associated with idling, gaping, or musing. The verb muse in this chain is not the name of a Greek goddess of inspiration. To amuse someone could mean occupying, distracting, bewildering, or even deceiving them.

How the meaning developed

Pleasant occupation eventually became entertainment, and amusing narrowed toward what entertains or makes people laugh.

In use

One means entertained. The other usually means confused.
Which fits: The audience was ______ by the comedian?

“Amused” means entertained. “Bemused” means confused or puzzled, although it is sometimes used informally for wry amusement.
A good joke amuses you. A baffling explanation may bemuse you.