A pixel has multiple elements producing red, green, and blue filtered output. A "hot" pixel has all of its elements fully outputting signal--thus outputting a "white" signal. With a long enough exposure time and a high enough ambient temperature, any and every pixel will eventually go hot, although temporarily. Usually the term "hot pixel" is reserved for defective pixel that is always hot.
A pixel may also have faulty elements so that it outputs only a single color or combination. That's a "stuck" pixel--a one-color pixel.
Or a pixel could be totally defective and produce no output at all...it will always be black.
With the high resolution sensors of today, you don't usually notice a single defective pixel, unless you're doing a lot of pixel peeping at 100%. More often, if you see it in a photograph at a "real" enlargement, you're seeing a clump of defective pixels.