I would say whether or not you're making any progress in solving/healing would be the difference. If that's too vague, I'd look at what is taking my attention and decide whether others think it is a problem or can be helped by continued working on it (my looks can't be changed so if I'm thinking about scars or physical features I don't like, that would be dwelling).

Basically, I'd say whether I'm thinking about the problem versus have a plan and am working the plan to help me heal/feel better. Just thinking isn't productive, there should be action of some sort in a positive direction.

With relationships, if I'm thinking about the other person and what they are doing and how they are making me feel, etc. that's dwelling; other people don't make us feel, how we perceive things is how me feel so if I'm not looking at my thoughts, perceptions and actions and trying to make myself better (instead of getting the other person to change) then I'm just dwelling on a problem. Dwelling is being "stuck". The only way to get unstuck from something is a lot of hard work and action. You've got to pull your "team" out of the mud. Running around trying to get someone else to push you, isn't working on getting yourself unstuck.