LINQ extension methods - Any() vs. Where() vs. Exists()

Question

Unfortunately the names of these methods make terrible search terms, and I\'ve been unable to find a good resource that explains the difference between these methods--as in

Answer 1

Where returns a new sequence of items matching the predicate.

Any returns a Boolean value; there's a version with a predicate (in which case it returns whether or not any items match) and a version without (in which case it returns whether the query-so-far contains any items).

I'm not sure about Exists - it's not a LINQ standard query operator. If there's a version for the Entity Framework, perhaps it checks for existence based on a key - a sort of specialized form of Any? (There's an Exists method in List which is similar to Any(predicate) but that predates LINQ.)