There are two types: technical and behavioral interviews. Technical consists of questions on math, brain teasers, puzzle, finance or coding. This is similar to first round interviews for jobs.
This is done by program faculty or alumni.
The second behavioral interview type is more common. It is còn ducted by program staff or directors to gauge your interest, fit for the program. Like why this program, what your desired career path, etc.
Each program will choose their own approach based on their selection criteria. Some programs have no interviews at all. Some may rely on applicants to submit recorded video of themselves.
Baruch MFE will have several rounds of technical interviews by faculty. Just like a job interviews.
UCB MFE will have technical interview by alumni followed by behavioral interview by staff.
Most other programs will only have behavioral interview.
Hope this gives you some idea what to expect.