In fact you aren't allowed to leave the country if the state doesn't allow it. You equate two concepts together because the words are similar (lord and landlord) but that's childish. It's obvious a lord back in the is much closet to a governments then a landlord.
Most serfs weren’t slaves[0], true. But in many areas serfs were legally bound to the land that they occupied. If that land changed hands, so did the serfs legally. That’s no slavery, but it’s also far worse than being a freeman.
In all areas they had fewer rights and more obligations than freemen; there’s a reason why being reduced to serfdom was often done out of economic need, and why freedom often had to be bought.
0 - Some types of serfs were literally slaves and could be traded as such. See Russian Kholops.