The animal was really a puma. The animal really was a puma.
What is the difference between these two sentences?
The animal was really a puma.
I would expect this to be a contradiction to a previous assumption. Something like:
We thought the animal was a big housecat but upon further inspection it was really a puma.
The animal really was a puma.
I would expect this formation when you are contradicting an incorrect disbelief about what the animal was (in other words the initial assumption was correct, but hard to believe):
Fred thought he saw a puma but the group knew pumas were extremely rare where they were. Once they got closer, they realized the animal really was a puma.