Grout along granite.

We have clear caulking instead of grout.

There is caulk that can be painted if you need to match a certain color. Some grout will expand and contract with temperature changes and also it will not crumble and fall out like grout. It will also be easier to clean. Just keep it in where the grout was and it shouldn't look bad if it isn't on the tile itself.

It is probably caulk, not grout. Just get a knife and scrape it out and replace with silicone caulk.

Yes you can use caulk there. You can get so many different colors of caulk now. Just use waterproof.

Since that's an expansion joint, I would think flexible caulk would be a better choice. Caulk comes in colors and you can also get clear.

I would stay away from clear caulk, as it ages it can turn yellowish looking. Choose a color that matches as closely as possible to the predominate color in your countertop.

Grout should not be used where a backsplah meets the counter. Should always be caulk. There always is some movement within the countertop and cabinets grout will always crack and break off. Just like wall tile against the tub caulk is always used.

I would try both colors and see what looks good in the situation you described, but with wall tile so much lighter, I think my tendency would be to use a caulk that matches the tile color as closely as possible. The seam I had in my mind's eye when I wrote my first reply was not a gap in the seam between countertop and tile backsplash but where two pieces of granite or stone meet - the countertop and the 4 inch tall matching granite or stone "backsplash" that is often installed as a backsplash rather than tile.