Are these screw holes? What material is the tile? A picture would be helpful too.
But generally speaking, you can use anything that won't look ridiculous. The tile should be well supported aside from the little hole, so there isn't a structural concern. There isn't a significant water infiltration concern on a kitchen floor. So it's really just about what will blend visually:
- Grout will adhere well and cure hard. Probably the best choice for blending with a stone tile.
- Caulk is easy to apply. Won't be as durable as grout but probably OK in the middle of a tile. If you're looking to match a glossy surface (like a white porcelain) this is a good choice. I'd recommend using a silicone or polyurethane based caulk here; latex/acrylic painter's caulk wouldn't stand up to much foot traffic.
- For the most durable but most expensive and difficult fix, go for a color-matched epoxy. This is the sort of thing countertop installers use at joints, and can be gotten or mixed in a big range of colors.
If you are seeing a caulk that's a decent color match, I'd probably start there. It'll run you like $5-10 a tube and if it sucks you can scrape it out and try something else. I wouldn't worry about kitchen/bathroom/whatever type, as these differences mostly have to do with microbial resistance additives and other stuff that isn't really significant if you're not caulking around a shower or sink.