Pictures help....
Generally one uses grout in between tile. It’s not a a structural material but more of an aesthetic, water sealing material. Between stones and concrete surfaces, one uses mortar to seal up gaps. Caulking is a flexible material typically used in an expansion/control joint between surfaces that can move relative to one another either from thermal expansion or hydrological expansion.
If the material between your coping and the bond beam (upper part of the pool wall) is a mortar and if the crack is minor (can’t fit a quarter in it), then you might not do anything at all as anything you try to fill it with will be difficult to work with and will likely stick out like a sore thumb. If it’s larger than that, then you might try filling it with some mortar but, matching colors and textures can be quite challenging. Filling a mortar crack with a caulking material will look terrible.
AT the end of the day though, you need to know why the crack appeared in the first place. If it’s just normal expansion and contraction, then trying to fix the crack may not be worth it as it will just crack again. If the damage is more extensive than that or you’re losing a lot of mortar from the joint, then that could be a material failure ranging anywhere from improper choice of material by the installer to water damage under the decking/coping. Again, pictures help a lot.