Sort of - cocoa is the modern API for newer applications, and least with the latest versions of OS X, the preferred one.
Carbon is a legacy API, used in OS 8 and 9 and is depreciated with the upcoming OS X 10.8 Mountain Lion . Some applications for OS X however continued using the carbon API until recently - wikipedia states older versions of photoshop, itunes and final cut were coded with carbon, though modern versions are cocoa based.
As a developer, you should be using cocoa over carbon, since cocoa supports 64 bits and well, isn't obsolete. In this case picking cocoa over carbon is a good idea.
As a user, this should be transparent to you, but you'd be using what API your software uses, assuming its supported.
I am guessing however compiling for either should work.