There is a difference. First and second are adjectives, and firstly and secondly are adverbs. But in usage they are sometimes interchanged (and often incorrectly). Firstly and secondly should really only be used for points of an argument or discussion--think "to begin with." You should never put the adverb form (firstly, secondly) at the end of the sentence and never use "firstly" unless there are more points. When you are denoting order, first, second, etc. is preferable and it can be placed at the end, as in "I did my homework first, then went for a walk."

I don't see any substantial difference between these words... they are of the same meaning. you should be consistent though in using these words like when you're using the adverb ending in "ly", the next adverb must also be of "ly" pattern. try to avoid this kind of usage: FIRST, I need buy new padlocks. SECONDLY, I've got to fix the roof before mom comes home. THIRD, I must seal the gate. FOURTLY, I'm gonna let my dogs loose. (seems prepared enough against the thief, eh?). I hope this one helps. :)

I agree with Kelli. However, I think the best policy is generally not to use firstly, secondly, or thirdly at all. Stick to "First", "Second", "Third". In general, I think "secondly" sounds a bit odd.

@ Kelli: just to clarify things, aren't that "first' and "second" can be an adverb too? What I'm trying to drive at is when the two words (first & firstly) are both used as an adverb, they seem to be the same. :)