For the sake of comparison, consider the Gimlet. It is a classic cocktail by all accounts with a well deserved following. While it is made of gin, it is not a Martini. Nor is the Tom Collins; despite its long and popular history.
Trendy variations abound: Appletini, Chocotini, Margaritini, Dirty Martini, etc. IMHO all of these are Kool-aid; sweet or flavored drinks with a touch of gin or vodka to appease the masses. These fruity flowery light weight bastardizations of the noble Martini will not be discussed, or tolerated, herein.
The only variations that will be discussed here will be the Vesper solely because of its history, source, and notoriety. And really, don’t we all have just a bit of 007 in us?