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.
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.