I would say they mean the same thing, but differ in connotation and register. "I've never been married" is pretty standard and neutral. Simply that the speaker has never been married before. "I never married" is a bit dated. For me, it conjures up the idea of a Regency novel dialogue. A bit old-fashioned, a bit of a higher register, and culturally, it carries with it a certain note of judgement. "And she never married" - at least to me - seems to imply that she failed to find a partner, or that something is wrong with her. Ideally, she'd be married, but unfortunately is not. Whereas, "she's never been married" is more a simple statement of fact.

Thank you Charles

Thank you MELISSA

Hi There are the same...

'I have never been married' implies the ending 'in my life' whereas 'I never married' sounds like you're talking about a missed opportunity at a specific moment in the distant past or a past life or something. Basically, no one would ever use the second phrase.