They were originally going to be identical (in the same way the fuzz and modulation pedals are) other than the hardware knobs but late on in the development they decided to pare down the features on Spectrum.
When you click on the Spectrum photo first, that should be filtering for Spectrum-only presets.
I’ll take a proper look tonight.
Just had a look on the mobile app and you are correct that C4 presets are appearing in the list. What will be the test will be what happens when I try to load one into spectrum that uses features not found in spectrum such as the square wave oscillator.
@AJ567, what happens when you try to load the patch “PWM” by jbharms1? That sound is composed purely of square waves. Does it work on your Spectrum?