Praise and blame is whether what you're doing is right or wrong, according to someone.
Fame and insignificance is whether a lot of people consider you special or not.
For example, if you have a Buddhist teacher, and your teacher tells you that worrying about fame is wrong, then you may completely abandon all concerns about being popular, but you may still be attached to receiving praise from your teacher and not receiving blame.
Or, if you so much want to deserve popularity, that you don't mind doing a crime like killing the Queen of England. You know you will get a lot of blame, but you still like the fame it gives you.
So the two issues are orthogonal, independent of each other.