Digital Frequencies vs. Sine Wave
Great question!

You can treat the square wave as a combination of an infinite number of sine waves. So, a 100 kHz square wave and a 100 kHz sine wave share the same 100 kHz fundamental frequency. But, what makes the square wave square is the additional sine wave components.

If you run a square wave through a perfect brickwall filter, all frequencies above the cutoff (or corner) frequency will be filtered out, and the square wave will just look a little less sharp. Move the corner frequency to 101 kHz and it just looks like the sine wave. But, filters aren't perfect, usually it will just attenuate the higher frequencies and not kill them completely.

For rise/fall times, this video might be of interest:

video: Oscilloscope Bandwidth and Sample Rate 

Basically, the faster the rise/fall time the higher the frequency component. So, filtering a square wave will slow down the edge speed. Also, if you're looking at the signal with an oscilloscope or multimeter, that scope/multimeter's bandwidth is basically a filter, so you may not see the exact representation of the signal.