Misuse of Same
The adjective same should modify a noun. If same is modifying a verb, consider changing same to alike or similarly.
It is common for people and their pets to look same.
Same could modify people or pets, but not look; use an adverb instead.
It is common for people and their pets to look alike.
Of course, there’s always the “to be/sense verb” rule to be considered:
They are the same.
There may be situations where the “to be/sense verb” rule doesn’t apply (English is notorious for breaking rules), so try a couple of wordings to see which sounds better. In situations where you’re writing informally, it’s alright to use same after a verb.