'Dark Jedi' isn't actually a phrase used in the films no it has no official meaning. I have always used it to refer to any one who was once a Jedi but who has fallen to the Dark Side.
'Sith' is an organisation. You are a Sith if you belong to it. The Sith are all Dark Siders but not all Dark Siders are Sith.
Well, they just call them Jedi.
But again, Jedi is an organisation. You are a Jedi if you belong to it. You could theoretically be on the Light Side and not be a Jedi. But as the Jedi are the only organisation in the Republic that actually trains people in the Light Side of the Force, the only way to do this is to be trained as a Jedi and then leave.
Well, people who don't actually 'have' the Force don't really have a side they are 'on', as such. Not in the same sense as Jedi. It's not about giving into your emotions or being at peace, or whatever. But Han is very definitely a good guy, and so if you talk about the Light Side representing good and the Dark Side evil then he is on the Light Side in a kind of metaphorical sense.