I was about to have a play on a guitar at a recording studio yesterday when I was told to use one amp not the other because the other was a bass amp.
I'm thinking about buying a bass but I only have a guitar amp.
What is the difference?

Bass amps can handle the bow-chicka-bow-wow much betterer.

I don't know the correct technical terms, but it's to do with frequencies, drivers, tweeters, horns and woofers. In differing quantities.

A guitar amp won't handle the low frequencies that a bass puts out, and a bass amp won't handle the higher frequencies generated by a guitar. And stuff.

guitar through bass amp may not sound great, but it will be fine, very HiFi sounding and rather un-guitarlike. If you use some effects though it can become quite good.
David Gilmour uses bass preamps along with an aresenal of effects.

bass through guitar amp = trouble ( likely ) as the bass frequencies can easily damage the guitar speakers.

Ok, now I know. Cheers.