Could that be viewed as a distinction without a difference? If I cannot move to another developed nation then is that different than not being able to leave my current nation?
Yes, it is extremely different except in the non-existent case of there only being two countries in the world.
I'm not sure I follow your line of reasoning. I'm not aware of any developed nation that an average person can freely emigrate to.
It is, it is a summary of the country's view on your rights. A free country would never try to keep you in.
If no country will take you, what is the difference from not being able to leave, in impact to the person wishing to emigrate?
While I agree that in terms of your choices there is no real difference, I think you should read about what happened when you wanted to go to a vacation as a (for example) Czechoslovakian citizen in the 1970's and what happened if you wanted out (hint: you would most likely die).