Generally in hockey 'Club hockey' refers to college hockey between intermural / pick-up hockey and serious varsity hockey. 'Select hockey' is kids hockey that is non-town hockey were you need make the team or get selected.

Since the inception of "club" programs it has been the same..

towns are non profit programs run by a board of vols.

clubs are for profit privately owned. hence the name private club.

Youth club hockety was around long long before college "club" even existed, well, maybe it was called intranurals, or "pickup" before they made it into a real level of college hockey.

Select hockey exited outside of club in towns, where kids would be selected for teams, some of those were non profits teams ran by a coach. Then the privatization and for profits boomed.