I noticed that the Hungarian rail site, MAV, was less expensive for the same trains listed on the Austrian rail site, OBB. Sometimes half. Didn't matter which direction you were traveling.
Then I went looking for a direct train to Munich and could not find one on the MAV site. I knew there are direct trains so I went to the German rail site and they showed a number if direct trains. Even the OBB site would sell me a direct train even though the train did not begin or end in Austria.
A little more digging and I discovered that the MAV site most often only sells international tickets that they can discount. Austria appears to be an exception to that.
So, if you are traveling to or from Budapest and you don't see a train that works for you on MAV, go to the rail site of the other country of your trip. The ticket will most likely cost more, but you will have more choices. Very strange.