The switch way numbering is based on the number of terminals.

A 2-way switch has two terminals and gives a closed (on) or open circuit.

A 3-way switch has three terminals and gives you one terminal tied to either, but not both of the other two.

A 4-way switch has four termimals and gives you two terminals which are each tied to the other two terminals and you can pick; these also give you a big headache when one switch of many fails and one circuit path is open, but many paths still work.

Or in other words if you're used to seeing switches from the electronics side of the world:

2 way: SPST

3 way: SPDT

4 way: DPDT

I once lived in a house with a 5(!) gang box with three of the switches wired to the upstairs hall light incorrectly and another switch upstairs. It was as big a mess as you'd imagine.

There are electronic three-way switches that have either a single button or an up/down rocker that always reacts the same way (up for on, down for off).

These are available in "smart"/connected form or regular electronics-only form. Example here:

https://www.amazon.com/Lutron-Incandescent-Single-Pole-Multi...

I agree with you and much prefer them to the traditional switches.

Get momentary toggle switches that stay in "off" position and toggle the light when pushed to "on" position.