**Jewish**: Is the person a Jew. According to halacha, this is defined by whether or not the person's mother was Jewish or they converted from another religion to Judaism (and the person did not convert from Judaism to another religion).

**Zionist**: Much harder to define, and different people would give it different meanings. My attempt to define it would be the belief that the Land of Israel belongs to the Jewish people and that it is the ideal place for a Jew to live. Secular Zionism and Religious Zionism would diverge on what is the basis for this belief (SZ would base it more on national history while RZ would base it more on scriptural and halachic sources).

So if a person says that they are not Jewish but are a Zionist, then they are saying that they do not fit the requirements of being a Jew (or even if they do, they are themselves agnostic and couldn't care well about in what category halacha would place them), yet despite this they believe that Israel is for the Jewish people.