There are many different relationships in our families. Some are decided by biology, some by the law or judicial rulings and some by the way we live. As a family historian, you want to record and describe each of these relationship.
The adoptive parents of a child may take over the legal responsibilities of the birth parents but the biological (or genetic) connection remains.
Examine carefully the tools that you use to find out what options they offer. Some modern software lets you set up multiple parent-child relationships that describe all this complexity.
Some people are concerned to know which parent should be the "main" one or even the "correct" one. The answer is that it depends what you are trying to show, If it is a question of property inheritance then the legal adoptive parents are the most important. But if you are interested in the possibility of inherited health issues, then the birth parents are the ones to consider.