nwales has already answered most of it comprehensively above.
Note: stress again: whatever local pass is NEVER valid for international trips, you have then to pay full distance from start and there have been regular reports of conductors checking this thoroughly and fining people. Thus this also excludes any Railjet, nighttrain etc.
Also any supplement or price for obligatory REServation still has to be paid-also if enjoying free travel-but thats very low price. For trains easiest to set up on the quite good machines and even cheaper untill day before travel. IF -in theory- such a RES is needed depends on what train and not short/long distance. Plus that such a short sector has plenty of other local trains. And indeed, on some routes some trains may even have a combo of better coaches as IC WITH and older ones withOUT. I think this is only on the Szeged line-but may have changed.
ALL those buses are done by Volan (=wheels), with the name of the province before. Also all smaller bus-only citybus networks. If you are busfan you may even hit the superold Ikarus (once Hungary´s pride as bus supplyer for all of communist East-Europe). Debrecen, Szeged and Miskolc have also trams (or even trolleybus) and their own city-owned ´company´. I am not sure if they also accept these passes. Volan has a few routes with an express part in it-also needing an extra supplement-just pay driver in cash HUF.
It may also be quite a challenge to find out how far those provinces/counties ´.meggye´ stretch out.
When I visited Hungary in 2017, rail travel was free to over 65s. Does that still apply, and if so, does it apply to people from non EU countries?
Has with that fares-reform in 2024 also been extended to anyone who can prove with legal ID s/he is 65 or older. Apparently-what I read in continental forums-is that it proved to difficult to distinguish as most ID cards are very much lookalike. For a while it was indeed EU-only as economy measure, as it does not affect me, I really dont know for how long that was.
To be pedantic, the REX6 train (Deutschkreutz to Bratislava-Petrzalka) stops at Sopron, but Austrian tickets are valid there (or at least I was told that at the ticket office).
To go via Sopron is indeed the route always adviced for those penny-pinching doing the Budapest-Wien run in stead of the direct route via Hegyeshalom. In the eyes/perception of the Hungarians-as these trains do no call at other stations in Hungary, they are not domestic. The VOR (north-east Österreich, around Wien=Vienna) tariff applies for that.
