Differences in voltage measurement at the input of a circuit
Ignoring the noise, it simply looks like the "B" waveform has a lower bandwidth, i.e. it's been low-pass filtered. The overshoot at the top is pretty typical for a band-limited step response.

The fact that there's oscillations that are visible on B but not on C might simply be the inverse effect, where things like wire inductance simply put a damper on some frequencies.

Since this is a rise time of in the order of 100 ns, we're dealing with frequencies of maybe 30, 50, 70 MHz that are attenuated in one path, but not the other. Honestly, at these frequencies, longer cables with mismatches can already produce resonant circuits, where you get strongly freqeuncy-dependent behaviour.

So: 

Make sure all your equipment is impedance matched, that involves cables, connectors, your device, and splitters, as well as the input settings on your scope. Make sure your signal generator is strong enough to drive your circuit, split off some energy for the oscilloscope B input, and also drive the probe.