I'm pretty sure by now the various "classes" of service offered by Lyft and Uber are instead just ways for the customer to donate money to Lyft and Uber. There's no difference in what kind of yahoo shows up in what kind of beater.
Assuming OP is in the UK, they're talking about hackney carriages which are subject to more stringent regulation than other private hire vehicles
https://en.wikipedia.org/wiki/Hackney_carriage
I think this would be similar to the medallions of yellow NYC cabs
It won't be a full-blown Hackney license, Hackney licensing is because unlike these "ride sharing" apps and what the UK would call a "mini cab" service, which require only a "public hire" license - the Hackney license authorises you to literally pick up strangers on the street, which was of course a completely normal way to use a taxi in a major city decades ago and is still somewhat common at say airports. That's what the glowing "Taxi" sign on the roof is for.
This needs more driver quality insight because e.g. passenger gets in your vehicle, you drive them to some secluded spot and their body is found the next morning - there's no records for murder cops to start from, unless there was a witness there may not even be a description of your vehicle. The UK has had this happen, but it's very rare because the sort of person likely to escalate to murder is not going to get licensed.
In contrast a mini-cab or Uber-style driver has records of who was dispatched to pick up somebody, where they were picked up etc. So if you take to murdering your fares the murder detectives will show up at your door with company records implicating you.
It varies a lot by country.
In my experience in west europe, booking a uber XL you usually get a full size van (vw caravelle/multivan, Mercedes v-class or a bigger Renault Trafic) with usually 7 to available seats.
Booking a uberXL in Mexico City gets you a miniSUV with only 4 available seats and if you get too much checked luggage it goes on a roof rack.
I pretty much just use it to book black cars these days - at least in my local city where those require licensed livery drivers. Good experience there for the most part. Most of the time I’m using Uber it’s either a business expense to the airport or I’m booking for a large party anyways.
That and I guess UberXL - otherwise it’s pretty fungible.
The interesting bit is that black is often pretty much the same price a UberX about a third of the time.