Are there different kinds of stroke?

Yes. Strokes can be classified as hemorrhagic or ischemic. A hemorrhagic stroke is where there is bleeding in and amongst the environs of the brain. Ischemic strokes are the result of blockage or diminished flow to regions of the brain. Ultimately, a stroke is a pathological alteration of brain blood flow.
Yes. Most strokes are either ischemic (lack of blood flow) or hemorrhagic (ruptured blood vessels). Roughly 80% and 20% respectively. A few cases are due to other causes such as asphyxia, hemorrhage, poisons, etc--but most of them also produce damage by interfering with brain oxygen metabolism.