Beyond being set in the future, there was no stated connection to Tom Corbett, though they do seem to be part of the Space Service.
...which many attribute to causing the producers of a new show to cast him as their campy caped crusader!
BTW, in a weird bit of comic numbering, this second series' #1 is Tom Corbett's first #1!
The earlier series (from Dell Comics) began with #4 since the first three issues were part of the Four Color series (#s 378, 400, and 421) which was used to test sales for a particular project or licensed property before giving it an ongoing series!