There absolutely can, and in many cases should, be a difference between your blood family, and your adult family.
The former was chosen for you. The latter should only be chosen by you. I can easily tell you that excising certain siblings, aunts and uncles, and a specific cousin, from my life, my life has far less stress than it used to in my 20s. Now that I tell people that "this is my boundary, try to cross it at your own peril," and actually hold the line, I have far more family than what I was born into.