A parent is a person who had sex and created a child. Only to this child would this person be considered a parent.
Additionally, when a child gets married they inherit their spouse's parents as their parents. We call this "Step Parent" because the relationship is different to us then the parents that created us.
To me parents are parents with respect to the concept of "Child to Parent" relationships. The reason for this is simple. A single child is responsible for providing unqualified acceptance, love and tolerance toward their parents. On the other hand, a married child that doesn't offer the same unqualified acceptance, love and tolerance to their spouse's parents will cause problems for their marriage.
"Acceptance" is easy to understand. You don't choose your parents, you simply get them handed to you. Like it or not, they are your parents. They have become a delicate part of your life's experiance. You can't hide them, you can't get rid of them, you can't deny them.
"Love" is a bit more complicated. We are created with a natural desire to love our parents. It's common knowledge that the secret to a happy life is to build on this natural desire to love to a point where we love all things. The more we love, the happier we are. The less we love, the less happy we are. This is a fact of life. To not provide unconditional love to our parents will result is a less happy life for us.
"Tolerance" is also complicated. Tolerance is a personality trait that people learn in order to get along with other people. In the normal course of daily life we usually learn to tolerate those things that we can't avoid or change. If a co-worker does not believe in God and you do, it doesn't make sense to make a big deal out of it, you tolerate it. Parents are no different. As a rule, you're not going to always like what they "Think", "Say", or "Do". It makes no sense to try and get them to think, say, or do differently because this approach does not work ever, and I mean never.