I’m assuming that you were asking about these two examples:
A) Des Schafes Wolle
B) Wolle des Schafes
and I’ll add a third option
C) Wolle vom Schaf
A, B and C may mean that the wool is still attached to the sheep, and they may also mean that the wool is already sheared off.
Actually, both A and B use the same grammatical structure (the genitive case), and particularly A sounds oldfashioned.
C replaces the genitive case with the preposition von, which is very common.
Now, let’s assume that example A should actually have been
A) die Schaf(s)wolle
This implies that the wool has already been sheared off.
This is also a generic term you might find for balls of wool (Wollknäuel) in the store, if they are not labelled more specifically (like e.g. Schurwolle).
In your example A, you mention *Schafes Wolle (with s), or better: Schafswolle, which is equivalent to Schafwolle.
Here the s would be a fugenlaut (epenthesis).
There are many epentheseses in German, and while it’s possible to write Schafswolle, using a nullfuge (no letter between Schaf and wolle) is more common.