What is the difference between method syntax and query syntax?

This is LINQ (using query syntax):

var _Results = from item in _List
                where item.Value == 1
                select item;

This is also LINQ (using method syntax):

var _Results = _List.Where(x => x.Value == 1);

It's interesting to note that both of these flavors will end up producing the exact same code. The compiler offers you a service by allowing you to express your wishes in the manner that you prefer.

And this is a lambda:

x => x.Value == 1

When you choose to use method syntax, LINQ is almost always seen around lambda expressions. But LINQ and lambdas are two totally different things, both of which can be used by themselves.

Update: As svick rightly points out, LINQ with query syntax is also implemented using lambda expressions (as mentioned earlier, the compiler allows you to write in query syntax but effectively transforms it to method syntax behind your back). This is just piling on the fact that both flavors are totally equivalent and will behave the same way (e.g. lambda expressions may cause closures to be created).

Both are Linq. The second one is using Lambdas.

Lambdas are the inline method type things that you are passing as a parameter to the Where function in the second example.

The difference between those two syntaxes is purely syntactic. The second linq style using method calls is how it works under the hood. The first is meant to be more user friendly/easier and the compiler converts it to method calls behind the scenes. They should work the same for any given query though of course the compiler may choose a sligthly different interpretation of a complicated linq query than you would when converting to method style.

This msdn article may be of interest too: LINQ Query Syntax versus Method Syntax. Of particular relevance is: "In general, we recommend query syntax because it is usually simpler and more readable; however there is no semantic difference between method syntax and query syntax."