I know that one of the differences between classes and structs is that struct instances get stored on stack and class instances(objects) are stored on the heap.
Sinc
How the compiler and run-time environment handle memory management has grown up over a long period of time. The stack memory v.s. heap memory allocation decision had a lot to do with what could be known at compile-time and what could be known at runtime. This was before managed run times.
In general, the compiler has very good control of what's on the stack, it gets to decide what is cleaned up and when based on calling conventions. The heap on the other hand, was more like the wild west. The compiler did not have good control of when things came and went. By placing function arguments on the stack, the compiler is able to make a scope -- that scope can be controlled over the lifetime of the call. This is a natural place to put value types, because they are easy to control as opposed to reference types that can hand out memory locations (pointers) to just about anyone they want.
Modern memory management changes a lot of this. The .NET runtime can take control of reference types and the managed heap through complex garbage collection and memory management algorithms. This is also a very, very deep subject.
I recommend you check out some texts on compilers -- I grew up on Aho, so I recommend that. You can also learn a lot about the subject by reading Gosling.