This is (velocity) = (displacement) / (time). s is used because of the Latin word _spatium_ for space. If I remember correctly, there was a difference between distance and displacement. (displacement is "net").
Displacement is a vector whereas distance is a scalar (similarly for velocity vs speed). Even if you restrict to 1 dimension there's a difference as displacement (and velocity) can be negative.
Slightly worse than that. That equation is always written as v = s/t. v represents velocity and s represents distance, for some reason.