... and we are talking about the removal of the *body* from the place where death took place or where the body lay between death and burial, rather than moving the *grave*.
As I have said in previous discussions (you can find them by searching for 'removed' in this forum), the column for 'removed from' in these registers tends to be superfluous for a large town or city. It would be more relevant in rural areas. When the clerks wrote 'Sheffield' I don't think they were necessarily thinking of the fine distinctions between townships within the borough.
I agree with Hugh. Most of my relatives as recently deceased as 1920's/30's lived and died in Heeley Parish but were interred in their family grave in Norton Cemetery (Norton Parish).
In the burial records all say "removed from Parish".