Is there a difference between a bass amp and a guitar amp?

The main differences between a bass amp and a guitar amp are the speaker size, the power output, the amp features, and the frequency range. Guitars use a higher frequency range compared to bass guitars, so guitar amps are designed to use smaller speakers (eg: 8-12 inch) and drive those speakers in different ways.

Is it bad to play bass through a guitar amp?

While guitar amps arent designed to handle bass input, it will work. But there is a risk you can damage your guitar amp with a bass at a high volume. Plugging a bass guitar into an amp is simple as both bass and guitar use the same leads. Simply plugging your bass into the guitar amps input will work.