Floor gap between tile and wooden floor
Where ever I had you situation, I used a colored latex caulk that was a close a match as possible to the existing grout in the tile floor. After all the caulk is leveled, everything cleaned up, and while the caulk is very wet still, sprinkle dry grout over the wet caulk and let that set on the caulk while it dries. It will give you the flexibility that the wood floor to move against due to seasonal changes since regular grout is not flexible enough to handle the wood movement.
If you choose you grout &quot;topping&quot; carefully, it should blend in fairly well with the existing tile grout.
After the caulk/grout combo is dried, use a vacuum to pick up most of the residual dust from sprinkling the grout. then with a damp cloth, carefully clean the rest of the haze that will be left over. If you choose you may want to tape either side of the joint before you start everything.
A tip that may come in handy... Latex caulk shrinks as it dries, so keep the thickness to a minimum to help reduce the amount of shrinkage. Do this by using &quot;backer rod&quot; to fill most of the depth of the gap so the caulk is only about 1/4&quot; thick, more or less. If the gap is already that deep, then no backer rod is needed. I am assuming the gap is 3/4&quot; deep, since the flooring looks like old school wood flooring.