> Schengen has independent of the EU status.

Schengen governs border controls, not the right to work and residency, which is a function of EU membership, not Schengen membership.

EEA gives you that, and Iceland is a member state of that too. So Iceland already enjoys this freedom.

I think Switzerland has a bilateral agreement with the EU (or via EFTA) that allows for free movement and employment of people, so they enjoy these freedom as well despite neither being in the EU nor the EEA (but they are a member of EFTA).

Employment too? I thought that was excluded. IIRC EU citizens can’t just work in Switzerland.

They can, pretty much like in the EU. There might be some technical differences, but overall it's both "right to work and stay if employed"

EU citizens do have a special status for work and stay in Switzerland that is barely more strict than moving within EU.

Yeah, I don’t know about what is included in the bilateral agreement with Switzerland. But at least in EEA (which is EU + EFTA - Switzerland) you are free to work in any of the member states.

The person you are replying said "moving" as in you relocate to another country. Not going on vacation. Swiss people can not just move to say denmark one day and start working there. They need work visas etc for that.

No, they don't. Whilst Switzerland is not in the EEA, it does have agreements with the EU which include FoM.

Switzerland is both a member of Schengen (meaning no border checks) and its nationals enjoy FoM (via bilateral arrangements). They don't need work visas.

Freedom of movement is not the same as Schengen.

I assume they're referring to actually residing and working in other EU countries, rather than just visiting.