In other words...
IDE Even your notepad is an IDE. Every software you write/compile code with is an IDE.
Library A bunch of code which simplifies functions/methods for quick use.
API A programming interface for functions/configuration which you work with, its usage is often documented.
SDK Extras and/or for development/testing purposes.
ToolKit Tiny apps for quick use, often GUIs.
GUI Apps with a graphical interface, requires no knowledge of programming unlike APIs.
Framework Bunch of APIs/huge Library/Snippets wrapped in a namespace/or encapsulated from outer scope for compact handling without conflicts with other code.
MVC
A design pattern separated in Models, Views and Controllers for huge applications. They are not dependent on each other and can be changed/improved/replaced without to take care of other code.
Example:
Car (Model)
The object that is being presented.
Example in IT: A HTML form.
Camera (View)
Something that is able to see the object(car).
Example in IT: Browser that renders a website with the form.
Driver (Controller)
Someone who drives that car.
Example in IT: Functions which handle form data that's being submitted.
Snippets Small codes of only a few lines, may not be even complete but worth for a quick share.
Plug-ins Exclusive functions for specified frameworks/APIs/libraries only.
Add-ons Additional modules or services for specific GUIs.