People often get caulk and grout confused, but there are major differences between the two and many situations where one is preferable to the other. Depending on the project you're working on, you may find that re-grouting rather than layering with caulk is the superior choice.
Caulk vs. Grout
Caulk is a latex and silicone mixture and is utilized in situations where a bond needs to be established between materials like ceramic, metal, glass or wood. Caulking is typically used as a measure to waterproof the joined areas between materials in places that are often wet, like a shower, bathtub or around the surface of a sink that is laid into the surrounding countertop. Grout is a cement-based mixture used to fill in the gaps or spaces between tiles, stone or glass, and to create strong bonds between joints on the same plane and should be used for large gaps between tiles or stones.
Caulk is preferable to grout in situations where two materials on two different planes are going to be joined together and where moisture in the joint area is likely. However, caulk can dry out and shrink, leaving the area exposed and susceptible to water damage. For this reason, it should not be used for large installations like bathtubs. In this case, grout would be the better fit.
Caulking Over Grout
Generally speaking, caulking over grout is not a great idea. Aside from the fact that aesthetically speaking this rarely works out, there are practical reasons why caulk might not be the appropriate choice to seal or connect two materials.
When making small connections, such as connecting the shower wall tile to the top of the bathtub, caulk is the perfect material. However, if you're attempting to replace the grout connecting the bathtub to the floor, or filling the space between two tiles or stones, your best bet is to re-grout it. If that is not an option, it's still preferable to scrape out all the grout and replace it with caulk versus placing the caulk over it.
How to Caulk
If you decide to replace the grout with caulk, be sure that you remove all the existing grout with a grout saw, and then vacuum any remaining grout so you have a clean surface. Then you can apply the caulk and smooth it out with the tip of the caulk gun, the back of a spoon or your finger.
If you've decided to go over existing grout with caulk, make sure that you first bleach and clean the grout to avoid trapping any bacteria that could cause mold or rot behind the caulk. Then apply the caulk using a caulk gun all along the existing line of grout by applying pressure to the trigger of the caulk gun and moving it backwards slowly across the surface of the grout. Smooth it out before pressing gently down on the caulk to push it deeper into the joint to give it a firmer connection.