A martini is comprised of gin, vermouth and between 0 and 3 olives.
If there is no vermouth it isn't a "bone dry martini". It's just "a glass of cold gin".
The modifiers "perfect" and "dirty" are also permissible when applied to to a martini.
If it's made with vodka, not gin, it's a vodka martini.
Other concoctions served in a cocktail glass are just cocktails. Which are fine, but please don't co-opt the name "martini" because it sounds cosmopolitan.
Wait.
Shit.