Here's my take on it, Pivots are a projected almost "theoretical" S/R level. Whereas horizontal or even TL S/R levels are based on trades / price action that has actually occurred.
Actually, except for examples provided via hindsight, all S/R is projected and theoretical. The point of the exercise is to determine those levels at which one might expect to see activity. It is more likely that one will find activity at levels created by prices paid rather than by an arbitrary line that springs from the mind of the chartist.