Cocoa is Apple's API to develop apps for macOS, formerly known as OS X.
Cocoa is a container framework, and contains three sub-frameworks.
Cocoa Touch is Apple's version of Cocoa to develop apps for iOS, watchOS and tvOS.
Cocoa Touch contains the same sub-frameworks, except instead of AppKit, it contains UIKit.
For Apps without any UI, it is recommended to simply only include Foundation instead of Cocoa
These apps are typically written in Objective-C or Swift.
The first thing you want to install is Xcode, Apple's IDE for building macOS, iOS, watchOS and tvOS applications.
It is available on the Mac App Store for free.
Pre-release test versions of Xcode are available from the developer website in the months following WWDC, which is required to test bleeding edge compiler/language features. These can be installed side by side with the production version of Xcode available in the Mac App Store.
After installing Xcode, you can start writing native apps for the Mac, iOS, watchOS or tvOS.
For details of getting started with a Mac App, see Introduction to OS X.
For details of getting started with an iOS App, see Getting Started with iOS.