The difference between them is that Earth-TRN588 ignores the continuity set up after Peter David finished his original run of Miguel with Spider-Man 2099 Vol 1 #44.

Marvel then gave issues 45 and 46 to other writers, followed by 2099: World of Tomorrow and 2099: Manifest Destiny, both of which were intended to finish up the Earth-928 Miguel and and all unresolved storylines, done without Peter David’s input.

So basically, Earth-TRN588 is “What-If Peter David kept writing Spider-Man 2099?”.