>>The general category is "string(ed) instruments". If you want to specify further then you would use "bowed string(ed) instrument". That actually should be corrected.
There's no difference that I'm aware of between 'string' and 'stringed' in this context; both can mean either Saiten- or Streich-.
In practice, when we refer to string(ed) instruments, we mean those in the string sections in an orchestra (violin, viola, cello, bass). Yes, they are technically bowed string(ed) instruments, but it's not usually necessary to specify that in most contexts.
Of course string(ed) instruments technically also include those that are plucked or hammered, but that's a less common context in normal conversation, even in musical contexts. You don't usually need to talk about all instruments that have strings as a group, unless you're studying acoustics, the history of musical instruments, etc.