"dramatic difference between the average Jew and a Zionist."

That statement is ridiculous.

Around 80% of Jews are Zionist worldwide.
Of the 20% who aren't, the majority are ultra orthodox who still believe Israel is their ancestral lands, they just don't believe in a secular state. They want the Messiah to come first and then make a theocratic state there.

The tiny fraction that don't believe in either of the above are those with less understanding or connection to their culture.

The promise to Abraham of where?
The escape from Egypt to where?
The land ruled by Solomon and David?
The return from Babylonian/Assyrian/Persian exile to where?
The place the Maccabees fought for self-determination symbolised in Hannukah?
The direction Jews pray to every day
The location of the place when we pray "Next year in Jerusalem".
The place where our whole calendars and seasons is based on
The place where some of our commandments can only be performed

The very essence of Judaism is the land of Israel. Zionism is self-determination in that land. Nothing more or less.