Talking about currying is not exactly the same as talking about closures. Currying is a specific programming technique that can be implemented with closures. Currying is the idea that if I have some arguments for a function now, and will have more later, that I can right now generate a closure that has pre-bound some arguments and avoid having to pass around the arguments everywhere. Thus a curried function is a specific type of closure. A closure is somewhat more general though - for instance you can have multiple closures that privately communicate through their shared environment.

The distinction may become more apparent in Perl 6 because they are adding support to give a direct syntax for currying. And you'll see that sometimes that syntax is enough, and other times you'll want to do extra work and create a closure by hand. (In Perl 5, of course, when you want to curry it is often simpler just to create a closure by hand.)