Handheld cutters are useful for small-scale projects where you might only need to cut a few simple straight pieces, such as up against a wall or cabinet. These are two-sided tools that resemble a pencil, only the tip of the "cutting" end is a carbide or diamond coated blade-like device that you score the face of the tile with. The opposite end of the tool is a U-shaped area where the tile is slipped between into the slot, pressure applied and the porcelain tile snaps along the scored mark.
Tile cutting boards are the preferred method for cutting straight cuts. They work through the use of a carbine or diamond-coated wheel blade that is attached to a handle on rails. The tile is placed on the platform under the rails and pressure is applied to the wheel as you push it across the tile. After that, pressure is applied to either side of the cut via a series of levers on the board to snap the tile in half across the scored mark.
Tile wet saws are used to make cuts around heater vents, doorways or other areas that are not straight cuts. While you can use a tile wet saw to make straight cuts as well as angled cuts and cut-outs, the preferred project for the wet saw is to make any cuts that cannot be made on a tile cutting board. Saws can be sold in chop-saw format, allowing for depth cuts to be made, and they are also sold in large-scale, rail format.
Rotary tools are specifically designed to cut round cuts or custom shapes in tiles with the use of a rotating carbide or diamond burr/bit, similar to how a dentist drill works. They can be used to cut any range of cuts, ranging from holes around pipe fixtures to edging out small areas to fit around a wall receptacle or a floor heater vent. They are not useful for straight cuts, but instead any type of round or awkward-sized cut that would be difficult or impossible to make on a tile wet saw or cutting board.