What's the difference between a Buffet and a First Class restaurant on Avanti West Coast trains?

Chris H's answer is a good overall one, but I'll add some specifics about Avanti.

First of all the slightly confusing messaging is as a result of private operators with slightly different and non-standard offerings trying to fit the information into an inflexible database format designed in the days of British Rail when everything was standardised across the network. So this is why you might see some differences in terminology.

What other operators call a buffet, Avanti call "The Shop". This is located in Coach C on Pendolinos and Coach D (and K) on Super Voyagers. It's more self-service than usual buffet counters which is probably why they've gone for the different name. They usually sell a well-stocked range of drinks and snacks, and a less well-stocked (often half of them are sold out...) range of hot snacks - the sort of thing you might have for a light lunch, things like hot sandwiches/paninis, maybe a pasta or rice meal, maybe some instant porridge type thing. Basically anything that can be made easily by microwaving it or pouring boiling water in it is the sort of thing you'd expect to find in terms of hot food. A sample menu is available here.. The Shop is available on all Avanti services, though of course might occasionally be unavailable due to staff shortages; I tend to find it to be very reliably available though from personal experience.

Since COVID, Avanti have also been offering at-seat orders from The Shop throughout the train. My experiences recently are that this is available on about 50% of trains - this is presumably dependent on enough staff being available etc. You can simply go to https://atseatorder.co.uk from the on-train WiFi and place an order to your seat.

In first class on all their trains out of London now (even at weekends), Avanti offer at-seat dining included in the ticket price, including alcohol as well. You just have to wait in your seat and the first class host will come round and serve you; though if you're making a short journey it can be helpful to specifically ask if you can get food; sometimes they won't if the journey is too short. This is honestly nothing to write home about but is certainly a step up from the hot offerings in The Shop. While microwaved dishes are still the majority (the main exception usually being the full breakfast on Pendolinos only) they're usually not too bad, in my experience. Weekday Pendolino menu; Weekends and Super Voyagers (microwave-only) menu. I have been on trains recently where the first class service has been unavailable due to staff sickness, in this case you are entitled to a refund for the difference between first and standard class. Which is a pretty good deal since you still get a first class seat without paying the Standard Premium supplement!

Avanti have recently introduced Standard Premium as a third class in between Standard and First, which gives you a first class seat but without an at-seat meal service; so Standard Premium passengers who want to buy food on board will also have to use The Shop.

To be honest, given the departure times I am certain that both of those trains will be expected to have The Shop and first class dining available, subject to staff availability of course. I suspect this is simply a case of data being out-of-date with the real world, or just inconsistent. For up-to-date dining information especially with the railway still feeling the effects of COVID you're likely to get a more straight answer on Avanti's website.

Of course all these menus are subject to change.