There is no single answer.

Like others have said, caulk (silicone) is available with many colours. It is available from same stores that sell tiles and grout (and other stuff for building the shower room from scratch).

In a normal bathroom, the stuff (grout) between tiles is porous and let's water flow through it. It is not for sealing at all. Usually the caulk (silicone) is used on "moving seams" where grout would crack. This is seals between walls, between walls and floor etc.. Most times, caulk is not sealing anything. Water has path around it via the porous grout. Depends on place what the purpose of the caulk is. Most times there is polymer "water insulation" layer UNDER the tiles/grout/caulk in shower rooms, ending up to sever hole. This polymer water insulation has been added before the tiles to floor and walls (it is fiber enforced polymer stuff that solidifies into flexy rubberlike plate). Caulk is in this case for visual esthetics and mechanically protecting the actual water insulation layer.

I have built my shower room and sauna myself for my latest house, so I have practical experience. The best way for caulking has been to put painters tape next to the seam on both sides (leave a few mm from edge of tile), put the caulk in place with the tool (pushing it out from the tubular container), and use a silicone tool to form the caulk seam (the silicone tool has several radiuses - and remember to put water or soap water on the tool - you could use finger instead of tool, but tool is cheap and you have always same radius with tool). Then remove the painters tape (don't wait for silicone to harden, you have to remove tape after applying silicone) and you have a perfect seam with no smears.

I know pros do it without the tape, but I have made the best seams with the tape. It looks always perfect like that with no smears.

Try it out first somewhere else. If nothing else, take a cardboard box and make seams to the inside corners to try!