Hotspots Core is a Free (as in "free speech" and as in "free beer") & complete Google Maps marker manager for your joomla site. It is easy to install and configure, but it has less configuration options than Hotspots Pro. It is for those of you who need to show just a few location on a map & don't need all the fancy stuff.
Hotspots Professional, on the other hand, is the version distributed for a fee which has all the fancy stuff Google maps can provide. It ads support for KML (which would allow you to draw lines), it has custom tiles for people that have a lot of markers. Thanks to the "styled maps" support you can create an unique map that would match the color & feel of your website. It can also provide your users with information about the weather in the region, traffic etc thanks to the google maps layer integrations. If you are running a community website you'll appreaciate the integration with Jomsocial, CB & AlphaUserPoints(AUP).
You can see a comprehensive feature comparison of the 2 versions on this page.