OP here. Both of these words do a good job of describing what someone does at Hacker School. I think the reason we've shied away from them is because they can sometimes come off as a bit pretentious. Given how young we are as an organization, we want to make sure to be humble.
I don't know if you know Jake from Insight Data Science, but he calls his students fellows and his program a fellowship: http://insightdatascience.com/
Per the point you were making in your essay, though, he does this because most of his students are post-docs and (1) they understand what a "fellowship" is and (2) do not necessarily want to be a "student" again. To a postdoc, especially, student implies having to pay for it.
The other folks upthread are sort of missing the point, honestly, because when it comes to a word like "student," it touches on issues of identity and association. When someone (e.g., a friend) asks your students, "What are you doing?" they're going to respond with, "Oh, I'm an X at Hacker School."
You want X to be something the students feel comfortable saying to friends, families, and co-workers. Whether "fellow" is too pretentious or not depends on who your students are and who they'll be saying "I'm an X" to.
I do know Jake! "Fellows" and "fellowship" are really good choices for Insight, though, to be honest, I hadn't spent any time considering the choice until you brought it up. I almost certainly should have. I think your analysis of that decision is totally on point.
Thank you for taking the time to make such a thoughtful and considerate comment. You have gotten to the nut of what I was thinking when I wrote the post and said it more eloquently than I did.
I think that's a very insightful point, and I agree.
As a side observation, I think you can actually make "fellow" in particular a bit more cool/casual, especially since it is a rather ambiguous term anyway and there are many kinds of fellows working on many levels out there. All it reliably seems to connote a learning environment, some degree of selectivity in participation, and less structure than a traditional school program.