I think the main difference is that a 1 month sabbatical is typically over-and-above your normal holiday allocation. This can make a huge difference for some people, particularly people with families.

With a normal "x weeks" of holiday those weeks quickly get committed. Vacations with your partner, childcare during school holidays, etc. Having an extra month above that can free up time for learning, pursuing hobbies, travel, etc. that is much more selfishly focused on your own interests, which can be massively invigorating - essentially exactly what a sabbatical is supposed to do, even if I agree that it would be nice to be even longer.