The kid with the simple ear infection will wait longer in the ER. (Note that I added simple: if the ear infection is complex the ER may see the kid sooner, but those are cases where when Urgent care finally gets to the kid they transfer to the nearest ER)
Most "decent" urgent care facilities will triage. That's one of the reason why you're asked why you're there on check-in (and also to ensure you're not complaining of something acutely emergent).
Waiting time is a matter of how the facility is managed. If an ER is handling a lot of noncritical cases, they can set up a facility for handling those cases, which would look just like an urgent care clinic. In fact, I once had a minor injury and went to the ER, and was transferred to an urgent care clinic in the same building. I had insurance.
If your kid has a possible ear infection or broken arm, and you have insurance, you go to an urgent care clinic. If you don't have insurance, you go to a hospital. In all other respects, the care is the same.