Also, if an undergrad does research during the school year, are they expected to be as productive as someone working during the summer? Do professors calibrate their opinions of students to account for how many hours a week they've said they could commit?
I think the main question is a false dichotomy. Most students don't have a choice between either doing research over the summer or doing it during the year. As long as it doesn't interfere with your grades or other activities, more research is always a good thing, no matter when it happens.
That said, in my experience you should simply have a conversation with your professor (or direct supervisor, who will often be a grad student or post-doc) about time commitment and expectations. No one expects you to do the same amount of work in 10-15 hrs/week that you might do in 30 hrs/week, and no one expects you to work full-time while taking a full course load. As with many things in life, just make sure to communicate about expectations.
The somewhat flippant answer is that, if possible and blessed with the choice, you should do both. Gaining more experience is, generally speaking, a good thing. Now more specifically, there are some good sides and bad sides to both:
- Summer: Lots of time not dedicated to doing other things means, well, lots of time you can spend doing research. For many fields, experiments require large chunks of time, and it can be easier to find those in the summer, when you don't have to worry about making it to your next French class or whatnot. Additionally, there are lots of summer-specific research opportunities, ranging from field work experience to REUs, which may mean more funding, and which often mean people are "used" to having undergrad researchers around in the summer months.
- School Year: In some disciplines, summer is also very busy. For example, one of my field's major conferences is in the summer, meaning I'll be both gone, and distracted before and after. For some fields, it's also prime field-work season, which means if you're in a lab or a theoretician, things might get a bit lonely. Similarly, people do like taking vacations in the summer. It's also often easier to work in "Research for Class Credit" during the school year.
Also, if an undergrad does research during the school year, are they expected to be as productive as someone working during the summer?
Not if their supervisor is being reasonable. Generally speaking, summers are fairly unencumbered for undergraduates, in a way the school year isn't. If someone is balancing classes, exams, etc. it's fairly unrealistic to expect them to be as productive as they would be in the summer, unless their summer hours are extremely limited (due to say...funding).
Do professors calibrate their opinions of students to account for how many hours a week they've said they could commit?
Again, assuming they're being reasonable, yes.
Are you planning on doing research for a professor or independent research?
If the former, it's best to do what's most convenient for the professor. I've found that it can be difficult to do supervised research over summer because everyone really feels like it should be break. On the other hand, professors usually have a lot of other commitments that they've planned to cram into the summer, and they might end up not giving you as much feedback as you'd like. You should really talk to the professor to work it out.
I've noticed that professors will admit to being incredibly busy but often won't cut students slack unless something out of the ordinary has happened. But this is because (often times) they've hired a student to help precisely because they're too busy to do it. If they cut you slack, then their work won't get done.
If it's independent research - even if you're doing it for course credit - then I only recommend doing it during the school year if you're otherwise taking a relatively easy semester. Also make sure to plan to give yourself a break around midterms and final. If you want to write a final paper, get it done at least two weeks before finals. I've found that it's really best to do independent research during the summer, but that's only true if you're incredibly self-motivated and self-disciplined (though really you need those traits to do research at all).