They must show an identity card or passport when they cross the border into the Schengen area (or into Bulgaria, Cyprus or Ireland, the other non-Schengen states). Citizens of Schengen states must do the same when travelling to RO/BG/CY/IE.

In some places this is done efficiently — I'll bet Irish and Cypriot airports are fast — but at others, especially the land borders between Romania/Hungary and Bulgaria/Greece, there can be long queues.

Visas for foreigners are managed separately, so a Chinese tourist can take a holiday round Austria and Hungary on a single-entry Schengen visa, but will need an additional visa to enter Romania.

physical border control between them and their Schengen neighbours. note, "physical" - it doesn't affect their rights to go to or work or live in other EU countries, just how annoying it is to physically cross the border into the Schengen zone.