The equinox is the instant the Sun crosses the celestial equator. If the Sun were a point and Earth had no air, day and night would then be 12 hours each everywhere.
In practice daylight is longer on the equinox for two reasons: sunrise and sunset are timed by the Sun's upper edge, not its centre (about 16 arc-minutes), and air bends sunlight over the horizon (about 34 arc-minutes). Together they add several minutes of daylight.
The day when daylight really is 12 hours is called the equilux. It falls a few days before the March equinox and a few days after the September equinox in the northern hemisphere, and the other way round in the south. Near the equator the days never shrink to 12 hours, so there is no equilux at all.
Switch to Sun's centre, no air to see that, with the textbook definition, equal day and night do fall on the equinox. Equinox moments are accurate to about 10 minutes.