A squib is a partial detonation, or sometimes primer only. It can leave a bullet in the barrel and like you said, bad things happen with the next round.
A failure to fire is click then nothing. Bullet goes nowhere. When you manually eject you get a complete round that looks fine except for a dimpled primer (or rim) to show it failed.
I've personally only seen it with cheap .22 ammo... in which case you just try again and it usually works.