This is sort of a huge question. A huge generalization is that appellate work is much more independent/isolated and not as fast-paced. On the practice side, appellate work is much more research- and writing-intensive and much more independent - you sit in your office and work from the record, do research, write, and occasionally do an oral argument. An
appellate lawyer said to me once, "
appellate lawyers don't get out much." Trial work involves working with other people much more (you don't have any real contact with opposing appellate counsel the way you do with trial counsel), and is more fact-intensive. I mean, you have to know the record in appellate work, but the facts you can address are what's in the record - they've already been chosen for you, you can't add more. At the trial level you're looking for facts to use. Trial work can involve a lot of research and writing, especially in civil litigation, which is dominated by motions practice, but it's a different kind of research and writing. Criminal trial work tends not to have the same kind of motions practice as in civil, but involves working regularly with agents/law enforcement/victims (even if you don't get to trial). I mean, there are motions, they're just very different kinds of things (more about what evidence can be used/excluded than about saying, there's no cause of action here to begin with).
On the clerk side, both involve a lot of research and writing (if you're talking federal court - I'm not sure how much writing there is at the state trial level). In both, you're mostly sitting and your computer writing stuff. The difference is that at the trial level, you deal with trials, but they're not a constant - how often you have a trial going varies a lot, but you can go weeks without a trial. (Again, leaving aside state trial court, which I think is much busier.) So you have a bit more interaction with people, especially non-chambers people, as a trial-level clerk than as an appellate clerk.
I have no idea what the difference is for judges.
I think one generalization about skills is that appellate work requires really excellent, intensive writing and research skills. That's not to say that trial work doesn't require good research and writing skills, just that it's especially the case for appellate work. (Appellate work also generally requires an appellate clerkship.) The stereotypical trial lawyer charisma that sways juries is helpful in trial work, and you have to be able to make yourself understood by/appealing to juries, but if you don't have good trial strategy all the charisma in the world isn't going to help you. And if you go into biglaw/complex civil lit, you're very very rarely going to be before a jury. (Conversely, if you go be an ADA you'll spend all your time in court and writing will be a distant memory.)
This is really rambling because it's hard to generalize about trial-level work - it depends too much on what kind of employer you work for.