"Kein Zugang" and "Kein Zutritt" can both mean that you are forbidden to enter. See examples from the real world of signs:
As the Duden explains, both words have the meaning of entering (Betreten): http://www.duden.de/rechtschreibung/Zugang and http://www.duden.de/rechtschreibung/Zutritt. "Zugang" is even listed as part of the explanation of this meaning of "Zutritt":
Zutritt, der
...
Bedeutungsübersicht
- das Hin[ein]gehen, Eintreten, Betreten; Zugang
So, with regard to this meaning, both words are synonymous. All claims to the contrary are simply false.