Some pinpoints, some starbursts, why?

I'm no expert in this field but what I think happened is the the brightest stars that have flare were recorded on the sensor during the first one-two second period of the 13 second exposure while the camera was experiencing a small amount of shake.  The dim stars take longer to show up thereby were recorded after the camera settled down since they are mostly pinpoints.

Try the shot again only extend the tripod a short distance giving it more stable support and use a 3-10 delay on the shutter release if you didn't do it earlier.