Most of the people who think Israel should exist, and that is to say most people, don’t identify as zionists. Just because you believe in some basic premise of an ideology or a movement doesnt mean you are part of it. If you believe, like most Americans, that there should be some basic safety net that doesn’t mean you are a social Democrat, and when people refer to social democrats they probably aren’t referring to the trump supporter in Alabama who likes his mom having food stamps. Same with nationalists, if you believe that the nation should exist with borders that doesn’t make you a nationalist.

Generally the isms and identifying with an ism is about the movement. A movement away from the basic premises and understanding of that idea that almost everyone has accepted and towards an expansion of that idea, social democrats want an expansion of the welfare state, nationalists want harder borders and a stricter definition of a citizen, zionists want an expansion of Israel and suppression of the Palestinian cause.