Obviously, martinis are served in a martini glass. However, there are bunches of different martinis that could be made and served to patrons. There are also drinks that are served in a martini glass that are not martinis. Also, these glasses may also be called cocktail glasses instead of calling them martini glasses because other cocktails are now being served in this type of glass.
These other drinks are the Manhattan, Daquiri, Blood and Sand, and the Cosmopolitan. Sometimes, people are not aware of what the drink is that is being served. If it is served in a martini glass, it could be a martini, but it could be another type of drink. The lemon drop is also served in a martini glass.