An R-1 is a bar-type agriculture tire found usually on bigger farm tractors. (they can be put on any tractor) They offer the most traction in mud but wear quickly on paved surfaces, and really tear up grass and delicate ground.
An R-4 is similar to an R-1 in that it has a bar-tye tread, but it's usually a wider tire, and the treads aren't as deep. They distribute the weight over a larger area. Alot of full-size loader backhoes uses these. They probably are the best all-around tire for compact tractors, and most people use these. They do very well on paved surfaces and fairly OK on grass if you're careful. They also last pretty long.
I think the turf-tires are R-3's, (not sure). They're good on grass, and pavement, and not too awful bad for loader work in dirt, but don't offer alot of traction for ground engaging work. They do pretty well in snow removal when used with chains.
A word of caution. Be careful when changing only 2 tires on a 4wd tractor, especially when using different types. There is a specific ratio with regard to the circumference of the rear and front tires. If you change the size of either front or rear tires, the opposite tires much be changed proportionately, or you could damage your drive train.