My mom divorced my father when I was 2 and remarried when I was 3. My older brother was 6. Our younger sister was born later that year. We knew our new dad was our little sister's 'real' dad and that we had a different dad. We only visited with him (our bio dad) whenever we came back to the state he lived in (we moved a lot cause my new dad was in the navy).
Eventually, our father (bio) remarried and had another little boy and little girl. When I was 8, my step dad adopted my older brother and I, legally, after our father (bio) signed over his parental rights (and still owes child support for both of us). We had always known our step dad wasn't our bio dad, but had always called him dad. When he adopted us, we were allowed to choose whether we wanted his last name or if we wanted to keep our birth name. Our step dad was the one who we saw every day he was the one taking care of us, he was the one who supported my endeavors and provided for the family. I knew he wasn't my 'real' dad, and I always wanted to know my 'real' dad [I did later, and I found out personally what was so wrong with him].
My husband's ex married her lover a month after their divorce. Their one and only child was 4 when the new man came into his life and he was 6 when his parents were divorced. He was 7 when he met me. He sees his father (my husband) regularly; his father is very much an involved parent yet. However, he calls his step dad 'daddy' (encouraged by his mother) and refers to his real dad as 'daddy john' (suggested by his mother and step dad).
: My step son is now nearly 12 years old.He calls his step dad daddy and calls me, his step mother, Katreena (because his mom won't let him call me anything but my first name). At least his mother allows him to call his two sisters, sister.