Two 20-Amp circuits in one box for outlets
Well, you can run two totally separate circuits to the box, from two toally separate single-pole breakers. That way if one trips, the other does not. Nothing wrong with that.

You can also run a "Multi Wire Branch Circuit" (MWBC) from a two-pole breaker (a fault on either will shut both down) with a single neutral and two hots. The savings is not particularly large so you can go either way. If doing this, you need to pigtail the neutrals so that removing one outlet would not interrupt the neutral on the other outlet.

My personal preference with this sort of setup is to use different receptacle colors, though choice is limited without having the price get absurd (many colors are made, but some cost 10X what the "common" colors do) so some other sort of indication on the faceplate (such as actual labels) to indicate that they are different circuits (and hey, state what breaker number they are, too) is another approach.