This sounds almost exactly like a midterm/final question I had in an early CS class. I believe this is the kind of answer your professor (I'm guessing this is for a class) is looking for:
A logic error is when the program runs fine and does not crash, however it does not run the way it should because the programmer did not program what he or she intended to program. For example, a loop that loops an incorrect number of times would be a logic error.
A runtime error is something not picked up by the compiler at compile time, but is reported by the OS while the program is running. The most frequent runtime errors are reading a null pointer, stack overflows, segmentation fauilts, and unhandled exceptions. Runtime errors will always cause the program to exit immediately.
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