In the second type of science-fiction, the science-fiction provides the setting but has very little to do with the story. That is, the story doesn't grow out of the science-fiction. The science-fiction simply exists so that a story may be told in that setting.
C.J. Cherryh, Whedon's Firefly, Asimov (sort of) all fit into type 1. Star Trek (and occasionally Asimov) fit into type 2.
I postulate these types in response to my brother Eugene's post The Brave Old New World of Star Trek. While I agree with his description of the Star Trek universe as fundamentally static--and the Federation as an internally rotting utopia that finally, thankfully, gets the boot--I do not consider that the silly, even mind-numbing, philosophy behind the show has much of anything to do with the show itself. I think there are a number of us Trekkies who watch the show for its stories, not for its conceptualization of the future--just as there are a serious number of us who enjoy X-Files while considering the whole government conspiracy angle to be too too jejeune (however, the comparison is not really very fair; Roddenberry seems to have truly believed in his rose-colored concept of the future, but Chris Carter, like Whedon with Buffy, deliberately created a X-Files mythology, and the mythology itself is not jejeune).
In any case, for me, the point of Star Trek has never been to watch the Star Trek crew surviving in the Star Trek universe, but to watch old, old stories with classic structures (problem, climax, resolution) being translated into "sci-fi" (or quasi sci-fi) terms. The best example of this is the episode "The Offspring" where Data creates a child. The plot is from the Greek myth "Pygmalion" where the gods bring a statue to life. In this case, the "statue" is an android similar to Data but more human than Data can possibly be; like all good Greek myths, that situation ends with pathos. It is a terrific episode. There is also "Starship Mine" which is simply just the movie Die Hard, only on a starship not in a bank. Additionally, I've always liked "A Matter of Perspective" which is a murder mystery seen from several different angles. And I get a kick of "Royale" which is one of those you-have-to-complete-the-story-to-win episodes (and involves a you-have-to-beat-the-casino-to-get-out-alive subplot). Due to Picard's archaelogical interests, there are also a few Rider Haggard-type episodes.
It's one big borrower-fest! Which I don't mind and actually enjoy. I like watching old stories in new settings. I love reworked fairtyales (like Tanith Lee's version of "Beauty and the Beast" which takes place in the future and involves aliens) as well as Shakespeare plays set in the 18th, 19th, 20th centuries (anything but the 16th, which is good because 16th century costumes always look so uncomfortable). Voyager is somewhat of an exception since it has the underlying plot of the crew trying to get home. (Check this blog for an upcoming post on Voyager, and its underlying plot line.)
To sum up, most Star Trek episodes are individual stories that just happen to use the same setting and the same characters as that episode you saw last week. With that in mind, I'm not sure the comparison to Firefly is altogether fair. Allowing for the fact that Firefly is possibly the only perfect season 1 on record, it definitely belongs to type 1, presenting a plausible future based on present information/trends. Unlike Whedon's work, Star Trek also has no mythology (or at least, no mythology that anyone who reads history would take seriously). Most importantly, the static nature of the Star Trek universe is necessary. You can't borrow and rework individual stories every week if the universe keeps changing (yes, I know Whedon did it, but like I said, Firefly is the only perfect season 1 on record).
I won't go into the debt that science-fiction owes Roddenberry's attempt but imagine a world without Galaxy Quest, which is as much a tribute as it is a spoof. No Star Trek, no Galaxy Quest. Now, isn't that sad?.