Been in contact with both kinds of leader/bosses and decided when I became my own boss, that I would guide people as gently as possible. Emotions and all. What's the phrase - more bees with honey?
Gently is a way to go, better that than with a heavy hand. I think it's about setting the tone, the expectations.
I won't hesitate to act in respect of a team member who is not performing and have no qualms in cutting them loose with a clear conscience - that's a leaders responsibility to their team...but not before working to bring them up to standard using methods that empower them to want to lift performance rather than vindicively or through abuse. (The latter just disenfranchises the rest of the team as well.)
Anyway, it's a broad topic I've taken over thirty years working with and learning so a short comment can't cover it; thanks for commenting and it seems your team would probably survey well if asked about your management style which speaks highly of a manager.