OK,
GeForce are the main-stream cards from nvidia (the competitor is radeon from AMD). they are ment for (mainly) gaming, and the newest lineup is the 900 series, featuring the maxwell architecture. as well as the 900 series, there is the titan series, meant for the most enthusiast gamers. the newest model is the GTX TITAN X.
Quadro (firepro for AMD) is made for workstations and it has a few benefits over geforce. it has ECC RAM support, and the GPU's are cherry picked for the best performance. they usually have more RAM then GeForce equivalents (because they actually use the same chips as in the geforce cards), and they feature double-percision floating points capabilities, which is a more fancy way of rendering a 3d model. quadros usually also have more video ports on the back, and more mutli-display capability.
you can watch a techquickie video about geforce vs quadro:
https://www.youtube.com/watch?v=U5Npt1BSF04
tesla is just an acceleration card (literally, it has no video ports out the back), and the point of it is to cram as much CUDA cores into a card, that will accelerate anything you want, as long as it supports CUDA acceleration.
BTW, all nvidia cards (since the 8800GT) are using cuda, so they will accelerate using it.