They're all useful. Number theory tends to be a little more essoteric, but is useful for understanding things like the minimum number of bits needed to store (complex) information, or, in understanding how much accuracy you can rely on maintaining through a series of floating-point operations (and strategies to maximize accuracy by ordering operations differently).

The exact cource contents vary between colleges/universities but usually Number theory is about integers, e.g., prime numbers and such. In my university, a course that deals with floating point approximations of real numbers and the like is named Numerical analysis.