I’m from Israel, and no one is using “Zionism” in the second meaning.
Zionism is, by definition, support for Israel as a Jewish state.
There are those who say “real Zionism” is supporting settlements in Gaza and the west bank, but there are also those who say “real Zionism” is an Israeli state existing alongside a Palestinian state. That’s like a US democrat saying a “true patriot” would support supplying a social safety net for the well-being of all citizens, while a US republican would say a “true patriot” would support a small government that doesn’t restrict the will of all citizens.
Personally, I feel that referring to Zionism in general as support for Israeli control over the west bank and Gaza started as a (partially successful) tactic to de-legitimize the existence of Israel. Not saying everyone who uses the term incorrectly is an antisemitic or whatever, but that’s basically where it came from.