In long jump, does it matter how high you jump? What factors determine the span of the jump? 

Yes, in long jump, it matters how high one jumps. It is explained below.

For initial velocity u and angle of projection θ, the maximum height is given by:

h = (u² sin²θ) / (2g)    or    u² / g = 2g / sin²θ

and the horizontal range is:

R = (u² / g) sin2θ = (2h / sin²θ) × 2 sinθ cosθ = 4h cotθ

Thus, the span of the jump depends upon:

(i) height h attained      (ii) angle of projection θ.