In the UK, a "postman" is someone who delivers mail to homes and businesses (they don't hand out stuff on the streets). Sometimes they might bundle leaflets and flyers in with the "proper" mail, but it's not their main job.
In the UK, we don't really use "mail carrier" to describe an individual person, b
Yes it's used for jobs who describe people delivering something. I just made some suggestions, which were in my vocabulary knowledge. Great answer Mr Wordy!