Yes, I believe the origins of the sabbatical are in academia where it was intended to give people the ability to take an extended period of time away from their traditional role and try something different (often travel or an overseas post). This helped keep them fresh and allow them to broaden their range of experience without needing to permanently leave the institution. More recently, the term has been bastardized to a certain extent by start-ups who use it as a form of "bonus vacation" for long-serving team members.
Most jobs I've seen (in the USA) offer up to two weeks of "paid time off" which you need to split between vacation and sickness. The concept of taking more than a contiguous week off per year for an actual vacation must be pretty rare. Usually my vacation days get used for the purpose of running an errand or taking care of a sick kid.
Since becoming an entrepreneur, I have never had a "vacation" - Sure, I went to different places, but always with laptop and a bag full of assorted devices in tow. I was thinking of going back to a "regular job" for a while, just to relieve some stress. Alas, I had another idea and won't be able to rest until that is built :)
that's also what i thought -- vacations for me means a month away from work where i don't have to check anything work related (email, slack, pagerduty).
according to google, sabbatical is:
> a period of paid leave granted to a university teacher or other worker for study or travel, traditionally one year for every seven years worked.
It's paid leave because you're almost always expected to write or finish a substantial piece of scholarship. One month isn't long enough to write a book, so I don't think this is the model Basecamp is following