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Logic errors and run-time errors are sort of the same thing.
They both occur at runtime. A logic error means you accidentally expressed something that you didn't mean to express, or you expressed something that is logically incorrect and will produce undesirable results.
A run-time error can be produced by a logic error, I would say there are two types of runtime errors fatal, and non-fatal, a fatal error crashes the program, and non-fatal error (usually logic) returns incorrect results.
Run-time errors also encompass incorrect use of libraries and other bugs that might cause unexpected behavior.
I think Logic error usually is meant to specify that it is the fault of the programmer and not the machine or underlying system.
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