Thanks to the above advice, I was able (with difficulty) to book Budapest to Salzburg by train. As mentioned, the MAV web site (Hungarian Train System) was much cheaper than the ÖBB web site (Austrian Train System). 69 euros vs 41 euros for date next month, 2nd class, non-refundable, one way, direct. The MAV web site is a challenge to use, specifically when paying you must enter your "billing address", but "USA" is not one of the available billing address countries. I almost gave up, until I learnt that entering any country is fine such as "Egyesult Kiralysag" (United Kingdom in Hungarian), as it makes no difference to the booking or payment what you enter! Thank you "Seat 61" - "A beginner's guide to Train travel in Europe". Then I could proceed with payment and booking.