Orthogonal to the JRE versus JDK dichotomy, there are two types of Java release that are widely available:
In functional terms, there is little difference between a Hotspot release and an OpenJDK release. There are some extra "enterprise" features in Hotspot that Oracle (paying) Java customers can enable, but apart from that the same technology are present in both Hotspot and OpenJDK.
Another advantage of Hotspot over OpenJDK is that patch releases for Hotspot tend to be available a bit earlier. This also depends on how agile your OpenJDK provider is; e.g. how long it takes a Linux distribution's build team to prepare and QA a new OpenJDK build, and get it into their public repositories.
The flipside is that the Hotspot releases are not available from the package repositories for most Linux distributions. This means that keeping your Java software up-to-date on a Linux machine is usually more work if you use Hotspot.