True emergency rooms here can be clogged, but in my experience, only at the specialist places (as in, if you go to a children's hospital in the middle of flu season, they can be backed up). What used to be an issue here with ER (as in, the uninsured would go to the ER and elect to "not pay at the time of care" because they weren't going to pay at all) has been dealt with effectively.
Friends who went to the UK described where they went as an ER, but this is all, like you say, a matter of terminology. The lines are also blurred here as health systems fight over patients. AT first it was ER traffic, then urgent care private (low quality in my opinion) centers opened, and then they had trouble with insurers and started offering things like discount cash prescriptions, which moved the insured elsewhere (if you paid for script coverage, the copay is still going to be less than discounted cash cost - paying $50 for a pair of scripts at the urgent care is more like a convenience charge.
The large health systems battled back by opening urgent care centers in retail places (and the quality is much higher), and since then, now all PCPs offices with more than a couple of staff in my health system have opened to walk in patients 6 days a week. So you can go to your own doc's office no appointment, but you may need to see someone other than your doc if you don't have appt. Small price to pay).
Then the battle started to come over surgery location. As hospitals lost ER traffic and had negotiated rates with insurers (That were low) the health systems started making outpatient convenient surgical centers (back to smaller buildings) in my opinion so that they could work around insurer reimbursement rates (the new centers started at a higher price - the patient doesn't know the difference as it's all insured).
Then, to squeeze out community hospitals or inflict pain on a competitor's larger health care location, the battling health plans here have started building mini hospitals, which would've been normal hospitals eons ago, but like 40 beds and an ER. Who knows where it will all end.
So, you can go to big ER, little ER, PCP office normal hours, private independent urgent care, or now urgent care centers within the network. The PCP office may not have an xray, but likely there will be a private imaging company in the same building so you don't even have to go to your car.
Personally, out of laziness, I like this. If I had a chance to get a few grand back or added to my paycheck and take a lower level of service, I'd take it for everything other than mental health parity. That law has been especially good because it puts people in talk therapy instead of on pills right away. You have the option for one or the other or both, but if you're battling insomnia or something and want to talk about the root of it, you can generally be talking to someone the next day or two.
The extra capacity (in my view) is wasted money, though. Most of the plans around here are not for profit, which means if they have earnings, they have to retain them or spend them within the system. I wish they had to give most of them back to the employers and patients.