Is caulk referred to as silicone caulk

A 5/8 inch gap is an awfully wide one to try to bridge with silicone caulk. Even with some type of filler I think you are unlikely to get a result that you would be happy with. At least I know I would not be happy.

Silicone caulk needs to be applied all at once to get a nice installation. First off it will not be reasonably possible to squirt out a 5/8 inch bead from a typical caulking tube spigot. Next consider that silicone material applied as a secondary application will not bond and adhere to previously applied bead that has cured.

If I had your issue I would be investigating filling up a majority of the gap area with a tile setting cement that is compatible with the backer materials behind your existing tile installation. I would then cut narrow pieces of tile (you could even band with a contrasting color) that you would set into additional tile setting cement such that it was flush with the existing tile surface. Once these strips were in place grout the spaces between the tiles and strips. Finally finish off with a neat narrow bead of the silicone material in the corner around the tub surface.

While I'm tempted to say the difference is just marketing hype, you can use either one, there is a very slight difference in formulation. The window and door stuff has slightly less petroleum distillates in the formula, according to MSDS information at nih.gov. Petroleum distillates will evaporate during curing, so I'm unsure why there's a difference. The difference is so small however, I'm confident you can use one or the other with no noticeable difference in the final installation.