Yes there were more than one specy, somewhere between 15 and 20. I don't know tge names of them all and the one most emblematic of xochimilco may very well be limited to this area but that doesn't mean the other species do not count, especially if they were all called axolotl by the indigenous population.
I see. Yeah there are 32 species in the same family and they almost all look like an axolotl before they undergo metamorphosis. The unique thing about axolotls is they are the only salamander species in the world that doesn't undergo metamorphosis (this is called neoteny). It'd be like if a frog just stayed as a tadpole its whole life.