It sounds like a semi-auto Norinco UZI where someone (for whatever reason) fitted an Israeli full-auto pistol grip to it, but with semi-auto parts. In the semi-auto pistol grip, I believe there is a blocking bar to prevent the switch from going into the "full-auto" position.
I'm not sure whether moving the switch to the full position (where full-auto parts were replaced with semi-auto parts) would cause the gun to slam-fire. If it does, it is just as illegal even if it won't truly fire full-auto.
Legal Full-Auto UZI's are a different breed. That's because there were several ways to legally modify them back in the day this could be done (and registered). Some were built on Registered full-auto receivers. Some were made by milling a slot in the bolt - these are called "bolt guns", because the bolt is the machine gun. Some were made by taking the blocking bar out of a semi-auto receiver. Still others were made by modifying the semi-auto bolt. I may not have covered them all. You really need someone who is familiar with full-auto UZI's to take a look at it.