I have a question. I thought one of advantages of becoming a member of EU is freedom of movement within the member countries. I went to Zagreb from Budapest on a train. Two groups of border control officials got on board, checked passport and stamped "exit" then the other group from Croatia checked passport and stamped "enter". I had go through just about the same process when I was going from Zagreb, Croatia to Ljubljana, Slovenia (this time I was on a bus).
So why do they do this when in Western Europe the border is always open?

You have your facts wrong - though there is freedom of movement by EU counry residents between EU countries this does not mean that there are alwaysopen borders - only members of the Schengen Agreement in theory have that with usually no border formalities except there always can be spot checks of persons and luggage (like sniffer dogs that sometimes greet Thalys trains from Amsterdam in Paris looking for drugs. Every non British citizen going into Britain is subject to Customs check and inspection and Immigration - most western European countries are in Schengen but not nearly every one:

https://www.schengenvisainfo.com/schengen-agreement/

In my limited experience, France also does passport control although they do not actually stamp your passport. IIgather it's due to the terrorism theyve encountered. They checked passport at the airport when we flew in from Frankfurt and again when we bused in from Geneva. But Switzerland did not care when we went into their side.

Hungary is in Schengen, Croatia isn't, so border formalities still exist. UK and Ireland aren't in Schengen, and when entering those countries from Schengen states, you have your passport checked and stamped if you are a non-EU citizen.

And folks requiring visas for Europe can I believe get one for all Schengen countries but need separate ones for Britain and non-Schengen countries?

Yes, you do, but Schengen and UK have different visa requirements. Those EU countries on the continent not yet in Schengen, such as Croatia, have aligned their visa requirement with Schengen in preparation for eventual participation.

Thank you all for straightening me out on this. Being in this area for the first time I did not know. In that case ( borders are not fully open among EU member countries) do Croatians, for example, need "permission" to move and live in a Schengen country?

Do not get the EU ideas of freedom of movement mixed up with the Schengen area.
https://en.wikipedia.org/wiki/Scheng..._with_opt-outs
https://en.wikipedia.org/wiki/Schengen_Area

You need to distinguish between EU membership and full implementation of Schengen acquis (agreement). As Croatia is a full member of EU, its citizens enjoy the freedom of movement, to live, work and retire throughout EU, with no permission or visa required. During the first few years of membership, there was some red tape but all has now been swept away. But since the country hasn't yet implemented the full Schengen rules, border checks still take place, for which EU citizens only require official ID, such as national identity card or passport.

Thank you all. Very interesting. Learning something new everyday.

There can always be occasional document checks. I've been checked on a train from Austria to Germany that started in Italy, and several young men were carted off at the first stop in Germany, presumably undocumented migrants.

I traveled from Hungary -> Croatia -> Slovenia -> Bosnia through Croatia by bus -> Croatia -> France.
Everytime I crossed the border, we had exit/entry border check. Croatia always stamped on the passport but Bosnia-Herzegovina never did. From Mostar to Dubrovnik by bus we went through these check three times! I probably have about 10 stamps from Croatia for these trips.