When Frum people talk about Zionism, they don’t usually mean either one or the other exactly although it probably has some aspect of both.
They are talking about some type of Religious Zionism which of course can mean many things.
At the smallest level, it would probably mean celebrating Yom HaAtzmaut in some fashion. At a larger level, it can mean sending ones’ sons to the army and/or daughters to Sheirut Leumi, it can reflect itself in the types of schools one sends his kids to and the type of Rabbanim he follows and the types of neighborhood he would live in.