We call them 'Optometrists' - the ones that can examine and treat eye conditions, The ones who fit and dispense glasses are Opticians.
The distinction between them is rather blurred and most use the term Optician. They usually operate in small practices with a few Optometrists travelling round different practices.
Generally, I would have to phone my 'Optician' for an appointment. Tablet? I simply sit in the waiting room till I'm called. No charge for tests or treatment - only glasses and even then I will get a copy of my prescription and can take it where I want to get a reasonably priced pair.
One day I suffered a a vitreous detachment that caused a retinal tear. I just walked into the nearest opticians, explained the problem and was seen right away. I was then referred to the general hospital where I saw the on-call ophthalmic surgeon. I had to return the following morning where my eye was repaired with laser stitching. Can't complain about the FREE service I received.