An open mic (also open stage) is an open stage: you sign up, get a time slot, and perform your own songs or covers. The focus is your set, not collective improvisation.
There is a sign-up list before or at the start of the night. Each name gets a few minutes in turn – often two or three songs. The stage has a mic, PA and usually an amp; a house band typically does not sit in with you.
Solo, duo or a small ensemble with its own arrangements is the norm. You choose the repertoire. After your slot, the next person goes on.
The audience comes to listen. Side-stage sing-alongs or jumping into someone else's song are not the default.
Open mics suit singer-songwriters, bands with original material, spoken word or music comedy. You want to present something you prepared.
If you want to jam standards with a changing line-up, a jam session is the better fit. The difference is in Open mic vs. jam session.
Karaoke uses backing tracks and on-screen lyrics; you do not need your own instrument. See What is karaoke?.
OpenStage lists open stages by city. Under Find events pick a city and filter by open mic.