This is really a case of semantics. I refer to my biological father as my father and to my step-dad as my dad. I agree with the usage referred to by Koth.
In the end what we, and the OP, are talking about is manning up! Barring medical issues, any adult male can produce offspring. Parenting a child requires more patience than I ever thought I had. And if you really want to impress your child admit to them when you are wrong. Make the time to spend time with your kids. They did not ask to be brought into this world. It is our responsibility to do our very best as parents, recognize when we are screwing it up, and make the changes necessary! Sorry, that's a mess of a paragraph!
I was raised by my step-dad starting around age 8, because my biological father was/is a pretty useless alcoholic! My wife and I got our son as a foster at age 5, and adopted at age 8. His parents were equally useless! He is 10 now, and I think we have learned as much about being parents from him, as he has learned about being a child from us.
In our situation, Matthew (Dennis at the time) required some pretty heavy discipline in the first three years he was with us, because he had never received any real parenting in the intial years of life. Times change, now I find that I need to curtail the discipline, show love, and understanding even when my first instinct is discipline. IMO kids need to know there are limitations, but they need to be loved more than anything else! Granted my situation is a little different in going from zero kids to having a 5-yo. But to me it just meant the learning curve was vertical, rather than the slight incline birth parents get to enjoy.
I could ramble on and on about this subject for many pages. It's hard for me to organize my thoughts here because they are so vast. In the end, learn from your mistakes like you expect your child to. MAN UP and be the parent your child deserves! Based on the OP, he is making the changes necessary to develop a relationship with his kid. I applaud him for realizing his errors and making changes. He and his child will benefit from it for the rest of their lives!