Basically there are two main types of marijuana: indicas and sativas. Indicas will usually produce a heavy stoned feeling while sativas will give you a more up high. Growers will often cross breed the different types to get a combination of effects.

Haze, Northern Lights, Trainwreck, White Widow, etc are different strains of weed. They can be types of indicas or sativas or a cross between the two. There are hundreds of different strains and new ones are always being developed. Check out http://www.overgrow.com/strainguide/ for some info on strains.

Shwagg, nugs, chronic, dank, mids, kind, etc are all basically slang terms for different grades of weed. For example Chronic, and dank usually mean high grade while shwagg is lower grade