forth means forward, foam is a substance like cream which is used to put out a fire.

Haha nothing really. Just, froth is more smooth.

Yes they are similar, but as explained, when you use a froth is when you are are talking about the top of a beer when poured. Fire departments put out some fires with foam. In that case, foam is a chemical.

In some contexts they're the same but in others they aren't. If you mean the stuff (the 'head') at the top of a glass of beer, then they're pretty much the same, although it's usually called froth. Froth is a bubbly substance that usually forms on the surface of a liquid. This can also be called foam. But, foam can be other things. E.g. rubber foam which is the sponge-like stuff you find in sofas. Or shaving foam - neither of these could be described as froth :)