What is the name for the boundary where two tectonic plates slide past each other horizontally?

A transform boundary - the third kind, alongside plates pulling apart and plates colliding. Nothing is created or destroyed; the plates grind past one another, which is why the San Andreas produces earthquakes and no volcanoes.

The grinding is not smooth. Friction locks the fault for decades or centuries while strain accumulates, then it slips all at once, which is the earthquake. A locked section that has not moved for a long time is not overdue in any comforting sense - it is a section storing more energy. The southern San Andreas has not had a major rupture since about 1680.

Most transform faults are not on land at all. They occur in enormous numbers as short offsets between segments of mid-ocean ridges, and mapping that pattern was part of what confirmed seafloor spreading in the 1960s: the direction of motion along those offsets is the opposite of what it would be if the ridge were simply a crack that had been displaced, which only makes sense if new crust is being made at the ridge segments.