Blur is a Mario Kart-esque multiplayer racing game with physics which are grounded in reality and graphics that are detailed and faithful to the cars and environments they represent. The main gamemode has you competing to finish first against other drivers in the same race, using power ups to get ahead or make others fall behind. The other game modes include a timed checkpoint race in which the track is scattered with nitro and extra time powerups and no other players, and "destruction", in which you use the bolt shooting power up to destroy as many enemy cars as you can within a set amount of time.
Nitronic rush is a stunting game with glowing and bloomy Tron inspired graphics in which every track's objective is to get from point A to point B as quickly and/or as stylishly as possible. To aid you in this, your car is equipped with a jump, wings, a boost, and mid-air directional thrusters. It utilizes an interesting physics quirk that lets you drive on the walls as long as you don't slow down too much.
I say again: Not in the slightest. Similarities end at "they both have cars and you go places in them".