Britain & America, two nations divided by a common language!
In the UK suspenders are used to hold up stockings, in the US they are called garter belts.
In the UK, a garter is, indeed, an elasticated band that goes around individual legs and is used to hold up stockings. Men also used to wear garters until recent times; knee garters were worn just below the knee by men under their suits to hold up their socks - they were a regular feature in bedroom farces and would be seen when the leading man (invariably) lost his trousers.
In the US suspenders are used by men to hold up trousers, in the UK they are called braces.
In the UK all hosiery whereby the stockings are attached to a panty are called tights. In the US, the sheer version are called pantyhose, whereas only the heavier denier opaque ones are called tights.
Americans do a lot of things differently to the rest of the world and get confused when confronted with terms other than those to which they are accustomed and all I can say to that is........KNICKERS! (lol)