"I would think that bios and software would be the same since they use the same sensors."
Actually for my mobo (A7N8X) and probably a few others, bios temps are read from the socket sensor while the software might be measuring socket and/or diode temps. For example, bios reads my cpu temp as 22C and case as 16C. MBM measures cpu (socket) as 22C, Diode as 18C, and case as 16C.
If you are sure that you've setup MBM correctly and that your mobo is supported, I see not reason not to trust MBM. MBM might just be using a different sensor. As you can see my diode temp is lower than my socket/bios temp.