Many people view shyness in a black-and-white context, thinking a quiet person is shy and a talkative person is bold/confident. Like most topics, there is a gray area. Being quiet doesn't automatically mean you're shy or insecure, and being talkative doesn't automatically mean you're full of confidence. Shyness has more to do with a lack of confidence and feeling awkward in social situations.
You can be a quiet/introverted person who has plenty of confidence and no feelings of shyness/insecurity. On the flip side, you can be a shy and insecure person who talks way too much. There are two people in my office who are extra timid, insecure, and shy, but if they get into a conversation with someone then you can expect them to talk forever. I'm sure most people know at least one timid/nervous person who will talk your ear off.
I'm a fairly quiet dude in general but I have no problem initiating conversations or joking with other staff members at work. I'm usually quiet because I get caught up in my own thoughts and I enjoy listening to other people's opinions. I add my input when I feel like it, but I see no reason to force my way into a conversation. Two of my close friends are quiet guys too, and they have no confidence issues either.
That's really all there is to it, but I can see why talkative/extroverted people have a hard time understanding the difference.