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How can I fill the blue space between two curves, for example $\sin$ and $\cos$, with random points? What if they are two BezierCurves instead of functions?

sine and cosine

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    $\begingroup$ Try this: Graphics[Point[RandomPoint[ImplicitRegion[Cos[x] <= y <= Sin[x] || Sin[x] <= y <= Cos[x], {{x, 0, 2 π}, {y, -1, 1}}], 1*^4]]]. $\endgroup$ – J. M. is away Apr 18 '17 at 17:28
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Here is a solution equivalent to the one posted in the comments:

With[{n = 1*^4}, 
     Graphics[{Directive[Blue, AbsolutePointSize[1]], 
               Point[RandomPoint[ImplicitRegion[Between[y, {{Cos[x], Sin[x]},
                                                            {Sin[x], Cos[x]}}],
                                                {{x, 0, 2 π}, {y, -1, 1}}], n]]},
              Frame -> True]]

random points between sine and cosine

(Note that this throws a redundant RandomPoint::unbndreg message, even tho bounds have been explicitly specified in ImplicitRegion[]. You can ignore it here.)

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