> I find it more satisfying and clearer to say it's when day/night are the same length everywhere on earth/for everyone on earth.

...except at the poles! (There the sun will appear to be moving along the horizon, and there is no day/night in the usual sense.)

And when you take the pedantry into account (top vs centre of sun, refraction) the length of the day/night is no longer the same around the globe, since the effect in terms of time is different at different latitudes.