components - Does the frequency of a crystal influence its height?

Here is a picture of two crystals:

Does the difference of frequency explain why the 6 MHz crystal on the right has a lower profile than the 5 MHz one ?

Answer

Influence, yes. Determine, no. For example, here's selection of shapes and sizes for the same spec crystals (and some ceramic resonators...)

The frequency is determined by the size, shape and cut of the quartz crystal inside the package, as well as where the electrodes are placed on it.