Can someone confirm that this is the type of bottom bracket that I need?

My current bottom bracket looks like this:



The writing on it says:

BB - CT91
Shimano Singapore
via 68 vB
BC 1.37x24
YL 116
L <--- ---> R

Also, is this meant to happen?:



The entire side of one side of it comes off!

I have two bike frames that I need components for. This bottom bracket is fine, so i'm putting it in one of the frames. I need another bottom bracket like this one for the other one.