There's not really a strict denotive difference between the two terms, as they are typically used in the community. Some people use them interchangeably, but I suspect that for most people there is a difference in connotations. I've known some subs who drifted between the two, depending on mood.

As a dom, if someone told me that they wished to be my slave for a session, my style would be pretty different than if they told me they wished to be my submissive. For the slave there would be direct orders, few questions, very little teasing and conjoling and more threats and punishment. The slave would be ridden hard and put away wet. With submissives, I like to foster inner turmoil and shame. I like to put them in predicaments and make them choose their own particular flavor of degradation or suffering. I like to tease and praise and give hope and take it away. I like to make them beg for reward or release.

Of course this is all at the hypothetical level. I would need to know a lot more about a person than whether they wanted to be a slave or a sub before I played with them, and all of those things would factor into the style of play. My point is just that to my mind, the differences between the two aren't as much about the duration or even the intensity of the arrangement -- it's more about the starting point of the arrangement. Do you start at "I'm a free-willed person who wants you to make me want to serve you" or do you start at "I'm your property to do with as you see fit"?

Personally, I prefer the submissive style. I like the idea that throughout the whole thing there is an internal struggle -- a constant choice to submit even though they might be thinking "I don't have to take this shit. I can walk out right now." To my mind, when someone declares themself a slave, they've already made the decision that they do have to take this shit. I don't mean that in some sort of dramatic way, like a slave has no self-esteem. I just mean that they've made the decision that they are going to act as if they are bound to servitude and are therefore that inner struggle between "I can't take this anymore" and "...but I really want more" may be less evident.

Anyway, that's just my take on the whole thing. For the folks who have completely different meanings for the terms, I'm certainly not suggesting you're wrong. That's just the interesting thing about language. And that was Tom's point: it's up to you (with or without other people, as you see fit) to decide what they mean.