As far as I know the only difference is functions defined inside a class are automatically made to be Incline which can speed up the compilation time slightly. But of course is only effective on short functions (approx 1 - 8 lines).
In general you should define your functions outside of the class as it improves the overall readability of your code so people can follow it easily. If you are just returning a member variable, define it inside the class...otherwise define it outside of the class.
It is common practice to not only define functions outside the class, but to put them in an entirely separate file which includes the header file. At compile time, you give the compiler two (or more) files: the file with main and the file with the file with the function definitions; the file with the class is inherently passed because it is included by the other two. The compiler generates two object files, one per source file, and then the linker combines them into a single program.
Basically no difference except for inlineness mentioned by @James2250 and the usual recommended approach mentioned by @Telion.
So if you want to try some class just to test some code you can use whatever approach you desire. If on the other hand need to write some code that it will be maintainable afterward stick with practices like separating your class declaration from your definition and use header files and source files respectively for this.
Alot of people including myself use the term "Method" to describe a function that belongs to a class. The term "Function" generally describes a top-level function, meaning it does not belong to a class.
For instance, many operators can be overloaded as methods but the ostream and istream operators must be overloaded as a top-level function.
It saves typing by defining methods inside the class but it is rather sloppy if the class is large. I have a few classes with 50+ methods and they would awful if they weren't separated.
By separating them you can give the programmer using you class just the header file and the object file. They can use the header as a reference guide for your class and can use the the object file to compile their own executables.
Then they can't mess with you code or break your object. : )