I suggest you look at this thread
It's a any vs where discussion
Here
is the content in case it gets deleted.
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.)