Stepper Motor Speed control using Driver IC
Yes, higher frequencies on the step pin for the DRV8824 will increase the speed of the motor by moving more steps per unit time.

With the TEA3718, the design topology is different. It's basically an H-bridge with some current alarms and variable drive current settings (INA and INB). Take a good look at the datasheet, particularly the typical application schematic (where you see that two of these ICs are required for a 4-wire stepper). Also, take a look at the Principal Operating Sequence to see how INA and INB can be used to implement half-stepping. You can absolutely vary the speed by varying the frequency of the waveform applied to the phase input of the TEA3718, but you will need to control this synchronously with another signal for the other phase.

Effectively, the TEA3718 is a bit more general purpose, and could easily be used to drive more generic loads (brushed DC motors, for example). The DRV8824 is more of an application specific IC.