what is the difference between application state and caching?

Application Object and Cached Object both falls under Server side State Management.

Application object resides in InProc i.e. on the same server where we hosted our application.
Cache Object resides on server side/ DownStream/Client Side.

Application Object will be disposed once application will stop.
Cache Object can be disposed using Time based cache dependency.

Only one user can access Application Object at a time hence we have to lock it every time we modify it.