Zionism is an ideology, Israeli is a nationality. One you get from birth, the other you don't.

The idea that all Israeli's must be zionist is ridiculous and demonstrably false.

An Israeli could settle for a two-state solution, or anything granting equal rights to both Palestinians and Israelis. A zionist could not, their movement is about creating an ethnocultural nationalist jewish state with as few Palestinian Arabs as possible. These aren't the same thing.