The aspect of the Parent state is really that of guiding appropriate and correct behavior which becomes the Adult state. While the restrictive, regressive components are those of the Child state.
The Adult state operates in the "here and now," while the unresolved conflicts represent an aspect of the Child part which exists in "then and there."
I work with the Adult part today by incorporating non-conflicted experiences from childhood---such as feeling joy, having fun, playing games, and solving problems as part of the healthy Adult. I use the term Child only when referring to unresolved conflicts from past experiences that intrude in the present. That is the "conflicted past" -- which is still present.
Issues that are resolved are truly past and usually do not arise at all.
Each of us can appreciate having an Adult self and a Child self. There are no perfect parents, and that follows too, that there are no perfect Adults. Some residual conflict from our childhood remains in all of us. Under certain stress--the degree of that stress varies from person to person---all of us are susceptible to regressing or falling back into operating from positions of past experiences.
We often tend to lean towards what is familiar even if it is not healthy.
The system for the Adult is "here and now" and for the Child it is "then and there."
Categorizing behaviors as arising from either the Adult or the Child aspects of a person helps to identify the origins of the behavior, assists in resolving conflicts, and thereby aids in the integration of the self.