To be clear here: The four freedoms are not related to the Schengen Agreement, they are guaranteed by the European Single Market [1].

[1]: https://en.wikipedia.org/wiki/European_Single_Market

My understanding is Schengen is about physical infrastructure and managing visas for third parties, and the EU about the actual rights for member state citizens. The UK was never in Schengen, and that meant that a French person coming to the UK could be stopped at the border, but they would be let through on the basis of rights enshrined in the EU.

For me in practice going to UK meant that I had to show my passport on the border, while nobody cares when I travel across Schengen. I don't know what would happen if they tried to hold me.

The biggest reason why Schengen Area is not equivalent with EU is that there are countries that are not part of EU, but are part of Schengen - Switzerland and Norway as well as there are countries that are part of EU but not yet part of Schengen like Bulgaria and Romania. I never was in Bulgaria and Romania, so I can't speak of practicalities.

And yes, Schengen countries have common visa policy.

You're right. There is border control in place between Romania and the rest of the EU.

Free movement of goods? Unless it’s Spanish wine. Or vegetables.

Or British meat..

https://www.france24.com/en/20160406-spain-summons-french-am...

https://www.catalannews.com/business/item/catalan-farmers-an...

https://apnews.com/article/8bfc0cd5b74bb238fce6c8c64af416d6

Those articles are 4, 9 and 30 years old, respectively. They also don't represent government interference in free movement of goods, more like direct action style protests. French farmers aren't known for being subtle in political matters.