I'm active on many discussion fora, but I see that people more often use the form forums.
Are both forms correct and adequate?
If so, why are there two forms for the plural of such a short word?
Although the proper Latin plural would be fora, forum has been adopted into the English language--and in most cases follows the rules of English pluralization. Similar changes can be seen with the adoption of other words like octupus (the proper plural would be more like octopedes, but in English we usually say either octopi or octopuses).
The current entry from the Oxford Dictionary says:
The plural of forum is usually spelled forums; the plural fora (as in the original Latin) is chiefly used when talking about a public square in an ancient Roman city.
Since you're talking about online discussion boards, I would use forums instead of fora when you are talking about more than one. An English speaker might understand fora, but it wouldn't come as naturally.