Do people and pets take on each other's personalities, or are people attracted to pets that are already like themselves?

I don’t mean the ones that look alike, but the ones who have similar personalities.

We have two dogs, a golden named Liberty, and a mutt named Annie. Liberty is my step-dad’s dog and Annie is my mom’s dog by default, long story. Each dog is similar to her master in personality and vice versa. Do they adapt to each other’s personalities, or do they attract each other because they are already similar?