As I put in my original post, I notice the distinction between the kinds of musicians mostly at dances. There are some musicians that can get the entire crowd dancing with fervent energy. Others can play the whole night and everyone just plods along. I can't put my finger on what exactly is different about the music, but I do know the way it affects the dancers. I'm not sure if it's a synergy being built upon, or just emotion being poured out thru the instruments.

Another thing I've noticed is that "musicians" tend to move when they play - rocking back and forth (guitarist), hunching shoulders and bobbing head (hammered dulcimer-ist (?)), swaying to and fro (bassist).

I do know that while playing orchestral string bass for 6 years in high school I was only playing the notes. After starting to mess with the guitar at one point I suddenly felt like the music was playing me (while playing a simple 3 chord song). Ditto with banjo - after 3 months of learning a bluegrass alternating thumb roll, it suddenly sounded and felt different. My pennywhistle teach once looked at me with slack-jawed amazement after I played a song I particularly liked. When I asked why he looked so dazed he replied, "That's the first thing I've ever heard you play that sounded like music."
I've wondered if this is difference between musician and person who plays, but anyone I've queried up until now just looks at me like I'm crazy when I draw a distinction.