In my experience, push on are splined to grip the splines and grub screw ones are made to accept the shafts that have one flat side. I'm sure they're not the only options though!
Yeah, if you don't have a flat edge on the shaft you should be able to nip the grub screw tight enough for general handling. If you want to abuse your knob you might find it slips round though. Many innuendo etc.
In my experience, push on are splined to grip the splines and grub screw ones are made to accept the shafts that have one flat side. I'm sure they're not the only options though!