I think Englishman put it well. Some feel the same way. Unfortunately, the Zionists have managed to fool people into thinking that one can be both.
A Zionist is one who believes in and supports pre-messianic Jewish sovereignty in Eretz Yisrael.
A Zionist is also one who supports the Zionist State of Israel. Here, it gets a little more gray-area, despite the absolute and innate tarfus of the State, as a non-Zionist may still support Israel only because Israel has imposed its ruler-ship over our brethren, so we want all our brothers and sisters safe and sound, BE”H, and that means working with what’s there, which is the Zionist State of Israel.