What is the difference between the 2 polyurethanes
One is waterbased and the other is oil-based. Both dry 'fast', one because it's waterbased and these finishes tend to dry fast by their nature, the second because it's formulated specifically to make it dry faster than it would otherwise (oil-based varnishes tending to dry fairly slowly, even in ideal conditions).
The best way to get a more complete picture of the differences is to read the full product descriptions on the Minwax site, as well as the directions for use since application and cleanup specifics are as important or more than qualities of the dried finish.
and which would be better because I am using the Mahogany color stain?
As both are recommended by the maker as equally suitable I think you can take it that they are.
Also neither can be definitely said to be better in the sense that this is partially a judgement call for each user to make for themselves, based on their own criteria.
For some people the drying time of the waterbased one will be the sole determinant of what's the best choice for them, as they simply don't want to wait 4-6 hours to put on each successive coat of Fast-Drying Polyurethane. Others will pick the waterbased one simply because they don't want to work with solvent-borne finishes for whatever reasons1 (and for the same reason they would probably have initially picked some other means to colour the wood). Still others will go with the Fast-Drying Polyurethane because they don't trust waterbased finishes.
Behind door number 3
Since you apparently haven't bought yet may I recommend you actually choose a third option: something else, i.e. a product from someone else.
Minwax by and large are the lowest rung on the ladder of finish providers, which is often reflected by its price2, and you'd benefit in a number of ways from trying out products from other makers.
I won't recommend a specific product as it's up to you to choose the type of finish you want to work with for starters, and then look at what's available (locally or via an online supplier3), has good reviews (ones you can trust), and that you find affordable. I will say that both Varathane and General Finishes make superior products to Minwax probably across the board, and either or both may be available from the same vendors that stock Minwax.
1 Maybe they hate the smell of organic solvents, maybe they hate cleaning brushes after using an oil-based finish (and it is often a chore to do it really thoroughly), maybe there's a baby or young child in the house and they don't want to take the chance with a high-VOC finish.
2 After all how often do we expect the best product, or even a reasonably good one, to be the cheapest on the market?
3 One that isn't currently experiencing delivery delays LOL