When reading the digital wave from a DAQ, should I be getting the same wave I'm generating to it?
The Nyquist criterion applies to pure sinusoids. The problem here is that a square wave contains numerous higher-order harmonics, at 3× the base frequency and higher, and these components are not being captured by the sampling. Think of it like having a near-ideal low-pass filter on the input.

For further information, you might want to look up the Fourier transform, and spectral content of the square wave.