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<T> which is similar to Any(predicate) but that predates LINQ.)