Hasselblad lens suggestions

[sothoth]

Hi,

I purchased a used Hassy 500 C/M body. I would like to purchase an 80mm lens for the body. There appear to be several types and I have done some reading on them, but hope a Hassy expert can clear something up for me.

What is the difference between these types? Are all compatible with the 500 C/M?
C
C T* (B50)
C T* (B60)
CF T*
CFE T*

It looks like the T* is an optics improvement, but the difference between the B50 and B60 is unclear to me, although I can see the lenses look different in pictures, I can't tell if there are any substantive differences in function and compatibility. I don't know the differences between the C, CF, and CFE at all.
Thanks in advance