you have got yourself a little confused here!
cars (which generally have curved upper surfaces and flat under surfaces) act like a airfoil (wing)... but a airoil gives lift not downforce, so as your speed increases so does your lift!!! we then put on spoilers, rear diffusers, flat undertrays etc etc. to try and to try and create downforce. there are two ways of doing this, reducing the amount of lift (the best way but you will never get downforce by doing this only) and also by increasing negative lift (this works as well but puts more drag on a car than just reducing lift as you are increasing drag on the car twice, first with the original lift and then again when you create the negative lift to counteract the positive lift). All of that confusing enough? I'll try and lay it down a bit more...
the aim of a undertray is to increase the air velocity and thus reduce the pressure (like you said) under the car and let things like spoilers still create downforce (not the whole upper side of the car, this will still be creating lift)... the only way to create negative downforce under a car would be to have the undertray as a reverse wing... but because the car is close to the ground this would actually not work as the air would increase in pressure as the undertray gets closer to the due to the volume of space reducing and actually create lift (would actually create more lift the lower the car got)
a rear diffuser is designed to create lower pressure (a fixed amount of air travelling below the car at a constant temperature is then allowed a higher volume thus reducing the pressure) below say a rear wing creating negative lift and higher pressure will cause "downforce"
a front splitter creates a huge high pressure zone from the car travelling through air being trapped above it thus creating drag and negative lift
also remember you can't create lift or negative lift without creating drag, but if you have enough power to overcome the drag then the benefits outweigh (pardon the pun) the drawbacks. This is why we get to jetset around the world in planes
its just simple physics and gravity using , but it can get confusing
a understanding of pressure in direct relation to volume and Bernoulli's principle is a must
as roy said, its very hard to explain without face to face with diagrams and hand gestures... if you want i might be able to do a diagram some time to try and explain the pressures put on a car body!!!