Assalamu alikum,
I am glad to clarify a few things that I hope they help.
- Mumin (believer) is Muslim, but a Muslim may not be Mumin.
- Muslim is the one who submits everything to Allah (God in Islam) and lives peacefully with people.
Mumin is the one who believed in Allah, angels, and prophets and follows and practices rituals regularly. Mumin is a pious Muslim person, or a typical Muslim.
On the other hand, someone who knows that Allah exists, and Muhammad is the prophet of Allah, does not follow Islamic rituals and not necessary and may pray from time to time. He is just a Muslim.
Mumin is "higher" and better than being a regular Muslim.
I hope you find this useful.
Regards,
Mohamed