No, not really. Water bottle would generally refer to a bottle used by sports people, such as athletes or cyclists, regardless of the contents. We would most likely say 'I'll just fill my bottle up' in general conversation, for example.If taking part in some kind of sporting activity we might say 'I'll just fill my water bottle up' but that is just because traditionally water is what you would fill you bottle with, whilst taking part in sport.

In a military sense - they have a a canteen. Here the bottles with a pop-top are sometimes called a sipper bottle. And sometimes people use a brand name for a water bottle. But - the most common is just water bottle.