A majority of wealth doesn't come from income so would never be touched by income tax. A "wealth tax" is just a broad term meaning that they should be taxed on the wealth fairly. Like capital gains for instance is a doozy. Way less taxation than what you likely pay (percentage wise obviously).
So "wealth tax" would include an income tax, capital tax, estate tax etc, all just at rates that are equivalent to how well the system treats them. They get a much larger advantage off the system that is set up than most others.
And the ultra wealthy don't even always have an income. You think Bezos has a salary right now that's significantly attributing to his wealth? Or Buffet or even Zuckerberg? I forget, his his salary still $1 a year? You want to tax only that?