We investigate the intra- and intermolecular correlations in semidilute polymer solutions by large-scale computer simulations and renormalization group calculations. In the framework of the bond fluctuation model we study polymers with chain lengths up to N = 2048 monomers and determine the intermolecular pair correlation function, the coherent scattering intensity, and its distinct part at all length scales. The simulations are compared quantitatively to renormalization group calculations of the universal crossover scaling function. Special attention is paid to length scales smaller than the density screening length xi, where the distinct part of the scattering function in the simulations is found to decay like q(-3-alpha) with a = 0.7 +/- 0.2. Various values of alpha (0 less than or equal to alpha less than or equal to 1) have been predicted by scaling theories, RPA and P-RISM theories, and we discuss in detail a short distance type argument leading to alpha = 2/v + omega(12) - 3 approximate to 0.8, where omega(12) denotes the ternary correction to scaling exponent. The scaling of the intermolecular pair correlation function on length scales larger than xi is also investigated.