I was able to install the same add-on in google chrome as in firefox. Do chrome add-ons have to be made especially for chrome, or do all firefox add-ons work in chrome?
Yes, they have to be made especially for Chrome, and no, Firefox add-ons don't work in Chrome.
Actually in Chrome they are called "extensions". And maybe it's possible to assemble the Chrome extension and the Firefox add-on in the same package? I guess that's what happened with your add-on? What particular add-on are you talking about?
For more information regarding Chrome extensions, see their official blog.