It's the same thing. COBRA means you continue any healthcare plan you had while employed, with the only difference being you pay the full premium rather than your company subsidizing it. But in this case, it seems Dropbox is still subsidizing it (if that is indeed what that sentence in the letter means)... so it is just continued health coverage.

The group plan covers employees. Former employees are not going to be eligible. Though the company can pay the COBRA premiums for the same coverage fairly seamlessly.

I was part of a group that split from a company, our new company paid COBRA premiums for our people until we set up our own group plan for the next year.