Typically, “platform” refers to the actual hardware/software upon which a piece of software is built or for which it is destined.
Example usage: “I built this app for the Windows platform.”
“Framework” refers to a collection of libraries/classes with the common goal of providing a scaffold on which to build software. Frameworks might completely alter how you implement your program or they might just speed up common tasks.
Example usage: “I built this app using an MVC framework for the backend.”
Example of using both terms together: “I built this app for Android platform devices using Xamarin, an implementation of the .NET framework.”