I get asked this question a lot and I thought I'd solicit some input on how to best describe the difference.
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Delegates are equivalent to function pointers/method pointers/callbacks (take your pick), and lambdas are pretty much simplified anonymous functions. At least that's what I tell people.
Well, the really oversimplified version is that a lambda is just shorthand for an anonymous function. A delegate can do a lot more than just anonymous functions: things like events, asynchronous calls, and multiple method chains.
I don't have a ton of experience with this, but the way I would describe it is that a delegate is a wrapper around any function, whereas a lambda expression is itself an anonymous function.
A delegate is a Queue of function pointers, invoking a delegate may invoke multiple methods. A lambda is essentially an anonymous method declaration which may be interpreted by the compiler differently, depending on what context it is used as.
You can get a delegate that points to the lambda expression as a method by casting it into a delegate, or if passing it in as a parameter to a method that expects a specific delegate type the compiler will cast it for you. Using it inside of a LINQ statement, the lambda will be translated by the compiler into an expression tree instead of simply a delegate.
The difference really is that a lambda is a terse way to define a method inside of another expression, while a delegate is an actual object type.
Heres an example I put up awhile on my lame blog. Say you wanted to update a label from a worker thread. I've got 4 examples of how to update that label from 1 to 50 using delegates, anon delegates and 2 types of lambdas.