I get asked this question a lot and I thought I\'d solicit some input on how to best describe the difference.
I assume that your question concerns c# and not .NET, because of the ambiguity of your question, as .NET does not get alone - that is, without c# - comprehension of delegates and lambda expressions.
A (normal, in opposition to so called generic delegates, cf later) delegate should be seen as a kind of c++ typedef of a function pointer type, for instance in c++ :
R (*thefunctionpointer) ( T ) ;
typedef's the type thefunctionpointer which is the type of pointers to a function taking an object of type T and returning an object of type R. You would use it like this :
thefunctionpointer = &thefunction ;
R r = (*thefunctionpointer) ( t ) ; // where t is of type T
where thefunction would be a function taking a T and returning an R.
In c# you would go for
delegate R thedelegate( T t ) ; // and yes, here the identifier t is needed
and you would use it like this :
thedelegate thedel = thefunction ;
R r = thedel ( t ) ; // where t is of type T
where thefunction would be a function taking a T and returning an R. This is for delegates, so called normal delegates.
Now, you also have generic delegates in c#, which are delegates that are generic, i.e. that are "templated" so to speak, using thereby a c++ expression. They are defined like this :
public delegate TResult Func(T arg);
And you can used them like this :
Func thefunctor = thefunction2; // call it a functor because it is
// really as a functor that you should
// "see" it
double y = thefunctor(2.0);
where thefunction2 is a function taking as argument and returning a double.
Now imagine that instead of thefunction2 I would like to use a "function" that is nowhere defined for now, by a statement, and that I will never use later. Then c# allows us to use the expression of this function. By expression I mean the "mathematical" (or functional, to stick to programs) expression of it, for instance : to a double x I will associate the double x*x. In maths you write this using the "\mapsto" latex symbol. In c# the functional notation has been borrowed : =>. For instance :
Func thefunctor = ( (double x) => x * x ); // outer brackets are not
// mandatory
(double x) => x * x is an expression. It is not a type, whereas delegates (generic or not) are.
Morality ? At end, what is a delegate (resp. generic delegate), if not a function pointer type (resp. wrapped+smart+generic function pointer type), huh ? Something else ! See this and that.