Mastermind groups are set up for entrepreneurs to come together and share their challenges with other small business owners. The purpose is to get suggestions and feedback to help overcome your challenges and have an informal board of advisors to push you to achieve your goals.
Business networking groups are usually more to meet new people and try and land new sales. Mastermind groups (the good ones) are not sales focused but instead try to help entrepreneurs get over their hurdles.
If you want more information I recently set up a Mastermind Group Blog
that talks about strategies for making a mastermind group work.