I think it depends on how I'm fishing them. Sometimes I'm fishing them with a tight line and active retreive -- eg stripping them in or swinging them -- then I would consider them streamers. However, I also sometimes fish them dead drift like a nymph. Sometimes I'll do both in the same cast -- ie, cast up or up and across stream, dead drift back, and then strip in on a tight line.

Harry Murray used the term "Strymph" to refer to those flies which could be fished either way and the Woolly Bugger fits in that class for me.