You are about right. I would make a slight correction since MSF and MFin are often used interchangeable. MSF/MFin is broad based (while still being graduate level finance work) and will typically place you into a wide variety of higher level finance. The degree is still quantitative and involves higher level math and stats, but no where near as high as a MFE/MSCF/MSQF program.
The MS in Computational Finance/Financial Engineering/Quant Finance are all really suited for engineers or mathematicians. You are going to be doing very specific jobs with a degree like that. Very lucrative, but very specific. Typically quant roles within a bank. CMU has an amazing program as do a lot of schools.
Master in Finance HQ