Is it true :
Cocoa is an application environment that consist of several Frameworks
and each framework consist of several API
Application Environment -> Framework -> API
Is Carbon the other application environment in OSX?
All things that allow an application to talk to a computer are an "API." That's a very broad term. It may refer to something as small as malloc, or as large as Cocoa. All of these are "APIs" in the broadest sense of the term.
On Mac and iOS, "framework" can have a specific meaning, which is a dynamically loadable bundle in a specific format. It can also have a broad meaning of "a collection of libraries that work together." There is a Cocoa.framework, but there is also the broader architecture of "Cocoa" which is a way of attacking problems together with a set of tools for attacking problems in that way.
An "Application Environment" is any environment that applications can run in. So Mac OS X could be considered an App Environment, or you might consider Darwin to be an App Environment, or Cocoa, or Carbon. It depends on what you're comparing it to.
The point in all of this are that these are not industry-wide well-defined terms. They're used to mean a lot of overlapping things, and they are sometimes used slightly different ways even within the Apple docs.
If you're looking for a good reference on general terms and how Apple uses them, you want to read Cocoa Core Competencies.