Races are the species that characters belong to. The basic D&D races are: Human, elf, Half-elf, Half-orc, Halfling, Gnome and Dwarf. Most of these races, except humans, are rare on planes other than the Prime+Material, though of course they're still available as PC choices. The basic Planescape races are: Human, Tiefling, Aasimar, Genasi, Rogue Modron, Githzerai, and Bariaur.
Nearly any race can be found somewhere on the planes. It is entirely possible to play a race not included as one of the standard planar races, in fact one of the advantages of the Planescape campaign setting is that allows players to mix character races from many different settings. Most of these creatures are primes that have journeyed to the planes, but some creatures actually have planar equivalents. Whether the race first originated in the Prime Material Plane or not makes no difference; after generations of living on the planes they have become part of the extended cosmos, gaining the benefits and downfalls of its true natives. Planar humans can be found in large numbers on nearly any plane, befitting their ability to adapt to any environment, but elves, dwarves, and other planar races exist as well.