I don't want to get too far into the assign vs convert discussion, save to say the difference is important and photographers should know the importance of assigning and when to do it.
Assigning is non destructive- the colours retain their numbers, but are remapped into another space , which may be preferable . Converting retains the appearance of the colours by changing their numbers to fit a new space. This is
imperative when images in different colour spaces need to be combined, however it may not be easy to go back home.
There are other situations where assigning or converting may be appropriate.
Both are equally useful. A bit like f numbers and shutter speeds. You need both but they are quite different.
It takes a bit of mental effort to get ones head around it. Joe's stuff is spot on , but must be read slowly and carefully.