Both are ways to install tile, marble, stone, or mosaics to walls and floors. I will explain to you each method of installation and then some options and pros and cons.
Thinset is a cement used to hold tile to a wall or floor. You buy thinset powder and mix it with water to the consistency of a paste, you then use a notched trowel to apply the thinset to the floor or the wall and in the case of some tiles you also apply thinset to the tile itself as well, glass tile for instance.
A Mud job is when you put down on the floor or wall a layer of concrete, this is fine sand and a Portland cement mixed together to make a consistency similar to wet beach sand. When you dig down in beach sand, right before you hit water, that would be the consistency of this mixture. That is one of the basic consistency mixtures used by most installers. This mixture of sand and Portland cement is then applied to the floor on top of a thin layer of thinset and is leveled out through a number of different methods pending on the installer style of installation. The thickness of this “mud” would be anywhere from 1” deep minimum to whatever it takes to float out the room level and smooth. The tile is then installed in one of two ways. The conventional “mud” job is installed while the mud is still wet or damp actually. You would "back butter" or apply another thin layer of thinset to the back side of the tile and then set the tile on top of the wet mud sandwiching the mud between the two layers of thinset. Then carefully tap down the tile in a number of different methods to level and at a pre determined elevation height or flush to the adjacent tiles. This method is for advanced installers and takes a lot of practice through a lot of trial and error.
Either way you go the preparation of the floor or wall is most important. The substrate must be secure especially the floor must have no give. So if you are installing over a wood sub-floor, you must make sure it is nailed off well and prepared. On a wood sub-floor a mud job would require a layer of tarpaper and then a wire lathe, and the wire lathe should be nailed off very well, the wire will make the mud somewhat monolithic and keep the floor solid. When using thinset over a wood floor you must use a cement board. There are many types of cement board and the best is one made for this purpose which comes in thicknesses ranging from ¼” to ½” and has a waffling pattern on it. This must be screwed down very well like every 6 inches or less to make sure there is no movement after installation of the tile. Then you thinset the tile onto this board. The next day after installation you can then grout the tile.
Pros and Cons
Mud-set is generally used to install marble or stone where they are butted up together with no grout joints. Mudsetting would typical eliminate any lippage and would keep the floor level and smooth.The drawback on a mud job is the thickness required to make it work. The minimum thickness would be about 1 ¼” and that could create an issue at doors and where other rooms join. The fact that you spread concrete out over the floor first also means that you can make the floor perfectly level throughout.
On a thinset job you must follow the contour of the existing floor and if the structure moves or has a lot of uneven pressure on it like equipment or a place where there is allot of traffic then the floor may move and could crack a tile or loosen the grout. If the floor is stable then thinset is actually a very good way to go. We use thinset when floor heights are an issue. The thin waffle cement board and the tile can be as thin as ½” so we can match up to an adjacent wood floor evenly and without a saddle. A smooth transition from room to room is always desirable. We make sure the substrate is solid by shoring up the beams and gluing and screwing down the sub-floor. Now is the sub-floor is concrete to begin with and it is very smooth and level, a thinset job would be a very good way to go because thinset holds so well. If the concrete is not smooth you can flash the floor flat with a thin layer of wet mud or you can have the floors ground down smooth with a machine made for this purpose.
In the end they are both excellent ways to apply a floor and thinset is the way to go on the walls. It just depends on the situation that you have in the area you will be tiling.