What effects do different flash diffuser shapes have?

The difference the diffuser shape makes is mainly the shape of the catchlights.

I.e – shoot a person with a square diffuser, you’ll get a square catchlight in their eye. Shoot them with something round, the catchlight will be round, which arguably may look more natural. On the other hand, square catchlight can look like a window, which is also neat.

There’s a section in this article on Adorama that shows the difference pretty well, specifically with this image: enter image description here

On a general note about diffusing, those small on-flash diffusers don’t do too much to diffuse though unfortunately. Of course it’s better than nothing but you won’t get anywhere near soft light if you’re shooting people. Shooting small objects though it can be useful and actually better than a very large diffuser, since that’ll soften the light too much and almost erase any visible shadows for a small object.