Part of the EU is outside the Schengen area, part of the Schengen area includes countries not in the EU. Stringent border checks for travellers within the Schengen area essentially do not exist (apart from heightened checks diue to security fears. Checks when travlling in the EU from Scghenfgen areas to non Schengen areas and vice versa are more stringent.
This may well be discriminatory but that is what the various countries have signed up to.

Today, the Schengen Area encompasses most EU States, except for Bulgaria, Croatia, Cyprus, Ireland, Romania and the United Kingdom. However, Bulgaria and Romania are currently in the process of joining the Schengen Area. Of non-EU States, Iceland, Norway, Switzerland and Liechtenstein have joined the Schengen Area. The border-free Schengen Area guarantees free movement to more than 400 million EU citizens, as well as to many non-EU nationals, businessmen, tourists or other persons legally present on the EU territory.