These are generalisations, and there will be exceptions to these, but basically..
Road tyres, are designed for Tarmac roads, and will always return quietest ride, and best MPG. They also offer the best grip on roads, but are heading towards being useless once you leave the hard stuff though.
Snow tyres, are road tyres, but have a special tread, that is designed to clear snow from the grooves, and some have the mountings for studs built in. They tend to be good in the wet as well, but owing to their design, have a shorter life expectancy on good hard roads. Can be OK on grass, but once you hit mud, then they tend to stop gripping as well.
AT = All Terrain.. A mixed tyre that is OK for light off road use, and has good road manners. Usually able to take a few more knocks, as they are designed to go over stones and rocks, and have better re-enforcing of the side walls, making them less like to be damaged by pot holes, and hard objects. The road noise is medium, and while not as economical as standard road tyres, are usually Ok. Basically, it's a compromise tyre for a soft roader.
MT = Muddy Terrain.. A tyre that will work in the worst of muddy conditions, but because of the type of tread needed, tend to have poorer, and sometimes very poor road manners. They also tend to be very noisy, and cost more in fuel to turn...
For general purpose, middle of the road easy to source types, it tend to come down to either General Grabbers ("Generals"), or B F Goodrich ("BFG's"), although, there are many many more, depending on where you live, and how much you want to pay. The main thing to look out for, if you do have an aversion to running remoulds, is a lot of the others tend to be just that, but some do make it hard for you to discover that they are...
