How old is this tile job? You have foundation issues that might need your attention if this has happened recently. I cannot believe that this has happened.
What I would do is to get one of the two products to actually caulk in the crack and make it less conspicious.
You might try 100% white silicon. apply in the crack and then wipe it off the adjoining tile. I am concerned about later yellowing though.
Exterior spackling might also work. you might even consider using pure white grout also.
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