ITRW, there are no true neutral zones between nations today. Neutrality would semantically seem to imply the exact opposite of being associated with a nation, though - and in practice it would be true no-man's-land, like the killing zone between the Berlins where any human presence would be an offense punishable by death without trial.
There are some disputed areas that the majority of this planet does not acknowledge as belonging to any specific state, usually on wasteland stretches of disputed borders. But somebody always makes a claim for such areas, even against majority/UN opinion or whatever...
There are demilitarized zones on Earth, though. The Wikipedia article on those displays a range of possibilities, including a sharp and well agreed-upon national border that just gets further padded (on one or two sides) by a zone where military presence is forbidden. A DMZ on Sinai today is an example of such, and Rhineland in Germany used to be a very famous example.
In the Trek case, we have to remember how the DMZ came to be. In "The Wounded", we learned the war was over but disputes remained. In "Journey's End", we learned a treaty would seal the peace by clarifying and geometrically simplifying the border, this achieved by ceding planets back and forth, with adjoining mass deportations of inhabitants. This did not work too well, so we next hear of the DMZ in DS9 "The Maquis" and TNG "Preemptive Strike", where worlds under clear-cut UFP and CU control still unhappily intermingle inside a zone where military presence is forbidden.
"Preemptive Strike" has our heroes describe the DMZ as being "along the Cardassian border", meaning a national border still exists. But is it to one side of the DMZ or meandering through it? In "Tribunal", Boone lives on "the Cardassian side of the DMZ", but does that mean Cardassian space beyond the DMZ or within the DMZ? There's still a bit of room for argument even with all the tidbits put together.
Timo Saloniemi