A Class 7 vessel was a Starfleet designation for a type of interplanetary sublight spacecraft, used during the 24th century. These vessels were typically armed with lasers and were manned with a small crew of about two dozen. Overall, they were slightly faster than Class 9 cargo vessels.
In the final draft of the script, the Atlec vessel was classified as "a minimum range combat craft of the Squadron Class, twenty-six crew"; it was armed with phasers. The script notes further described the spacecraft as being "even smaller and more outdated than Okona's" and that "[i]n scale it looks like a P.T. Boat pulling next to the USS Missouri."
As for the Straleb vessel, it was classified as a class four armed spacecraft. 
The term "Class 7 vessel" would seem to indicate ability, rather than design, as the two vessels with this designation that appeared were of the same class, but significantly different design lineages.
The Merchantman model from The Search for Spock appeared as one of these two vessels; a new model appeared as the second. Footage of the second model would be reused for the Antares-class Corvallen freighter in TNG: "Face of the Enemy", and later returned, slightly modified, as the Angosian police shuttle vessel in TNG: "The Hunted".