Grout is a bonding and sealing agent more closely connected with tile, while silicone is a more general-purpose caulk designed to help with moisture issues. In most projects, you will need to use both to create a safely tiled shower.
Grout
Grout is the mortar compound that you use to line the areas between tiles when you are installing shower tile. Grout lines can vary in size depending on the tile, but they are usually wider for ceramic tile and thinner for stone versions. Grout comes in a variety of colors to help you match its color to the tile. It also comes in both sanded and unsanded varieties. The sanding version is used with the wider ceramic tile grout lines, while the smooth grout is used for stone.
Uses
Grout is a necessary part of your tile shower -- you cannot replace all the grout with silicone. Grout is designed to cure into a firm line that keeps your tile in place and helps protect it from movement and moisture. It is often used in combination with a grout sealer in showers for added water protection. It is not designed to be flexible.
Silicone
Silicone is a type of caulk designed specifically for tile projects in high-moisture areas, such as showers. The silicone will produce a waterproof lining that is ideal for protecting the edges and gaps commonly present in the shower. It does not come in a variety of colors and textures for tile-matching like grout does, and it is applied like a traditional caulk instead of a mortar.
Uses
Silicone is ideal for use along the edges of your shower, where one tile surface meets another or when the shower meets the surrounding wall or ceilings. The silicone is flexible and will be able to absorb structural shifting in these places, while grout cannot. The silicone will also provide the necessary waterproofing layer in these sections that grout would not be able to offer.