Well, there are many different types of wine and cider yeasts. I keep a few on hand, but use mostly champagne yeast, cotes de blanc, and montrachet. They are cheap and convenient. The strains all ferment, but some will leave the cider a bit "fruitier" or drier than others.
From Jack Keller's website, here are some characteristics of some of the most common yeast strains: http://winemaking.jackkeller.net/strains.asp
I've never reused a yeast cake from wine or cider. I do it all the time for beer. The reason I don't do it for wine is because either I've used a cheap dry yeast and it's not worth it, or if it's a fruit wine, I have lots of gross lees in the yeast cake. I imagine you could do it, if you needed to, of you had a very expensive yeast strain you wanted to save.