A top is someone who is supposedly in control during a scene. A bottom is someone who supposedly gives up control in a scene. There is not necessarily a "relationship" outside of the scene. It doesn't always denote public play as some people do not play in public, but it does refer somewhat to a more casual acquaintance. It's more of a physical "control."
Some people use top and dominant as well as bottom and submissive interchangably, but there is a slight difference. Fetish bottoms are very much self-centered. You don't have to be submissive to be a bottom. Ask any dominatrix...they are approached by many males who are supposedly submissive but who really just want to satisfy their foot fetish or whatever other kind of fetish they have. The dominatrix is simply a means to an end. You also don't have to be dominant to be a top. If you're looking for straight lines, you won't find them here.
Submission doesn't necessarily mean having to do things you don't like. It's being under the control of another and making his needs a priority. Your pleasure is secondary. You find pleasure in serving his needs. This is not to say that you never enjoy yourself or that the dominant doesn't make sure your needs are met. It's an exchange. The control in a D/s relationship is more mental or emotional than physical.
If you have no desire to be controlled outside of the bedroom/scene, i.e. only submitting to play, you're a bedroom submissive or bottom. If you want your partner to have control in certain aspects or most aspects of your life, you're a submissive. If you desire a total power exchange or control in all aspects of your life, you're a slave.
No, you're topping. *lol* I don't know if I'm doing a very good job of explaining things.