When two things are so related it is situationally useful to think of them as one thing

An example of this relationship occurs in the Observer Design Pattern.

https://en.m.wikipedia.org/wiki/Observer_pattern

The names for the parent and child here would be subject and observer.

A different example, which puts more emphasis on the parent’s ability to control as opposed to the child’s ability to interpret, can be found in Control Theory.

https://en.m.wikipedia.org/wiki/Control_theory

Here the parent would be the controller. The child could be descibed generically as a dependent.

These are examples from the world of machines. The human world offers many more examples, such as master/servant, parent/child, captain/mate, etc. However, if the intent is to not anthropomorphize the description, electrical and computer engineering offers some possibilities.

In the first example, you have an observing relationship. In the second case, you have a controlling relationship.