Cocoa is the API, Objective-C is the language, and yes you will need to know both to program for the iPhone. Objective-C is easy if you already know C and C++. Actually the iPhone API is somewhat different from the Cocoa API used in Mac desktop applications, though very similar and exactly the same for a large subset.
Cocoa is two pieces: Foundation, which is low-level stuff non-UI stuff like strings, collections, networking, etc., and AppKit, which is all the higher-level UI stuff like views, window controllers, buttons, document management, etc. As far as I understand it, the iPhone basically works pretty much with all of Foundation, but has a replacement for AppKit called UIKit, which again is similar but has some differences (for one example, how to deal with multitouch events). So learning Cocoa with Mac desktop applications would certainly not be a bad way to get there, although you could just jump to iPhone coding directly.
But bottom line is you will need to learn Objective-C first. Apple has a pretty good PDF available on its dev site which will get you up to speed with that, then just start reading the documentation.