In the world of theater there are all kinds of tapes used for all kinds of things. You need to know what tape is used for what purpose, this sort of knowledge can be crucial at the right moment.
Spike tape is the most important tape in rehearsal. It is small in width and unusually thick and resistant. Spike tape comes in a variety of colors and is used to mark where furniture or set pieces go during certain scenes. Since there may be a furniture piece in a certain place during one scene but not in another. Traditionally once it has been determined where a piece will go the piece is "spiked" by placing two 90 degree angle marks on the back corners of where the furniture is. Thus the actors or crew can easily put it back in its position by following the marks. Spike tape is also used for taping out the area of the stage if you are in a rehearsal space. Its color variety can help to distinguish what scenes the furniture goes in.
Glow Tape is the next most important tape after spike. It is a special tape that as its name suggests will glow in the dark. However in order for it to work it must have absorbed some light before. This tape is used to mark areas backstage since it will be dark during the show and the actors will still need to see. Glow tape can help lead actors to places they need to go and can also warn them if there are steps or other hazards to avoid. It is also commonly placed on the back edges of set pieces so that the actors don't bump into them.
Gaff tape (or gaffer's tape if you prefer) is similar in design to duct tape and is often mistaken for it. However the outer layer of the tape is made of fabric, not vinyl, which makes it strong while the adhesive part of the tape is made from a synthetic adhesive that allows it to be easily removed with out damaging whatever it was stuck to. It's most common use in theater is to tape down cables that are running along the floor to prevent tripping or to hide it from the audience.
Painters tape (or masking tape if you prefer) is a tape that solely exists to mark off areas that should not be painted. The two most common colors are blue and white. The tape is brittle and weak and not very useful for anything else. On the bright side its weak adhesive allows it to be easily removed with out sticking to hard to surfaces.