What is it called when both hemispheres are getting the same amount of radiation from the sun?

It is called equinox. An equinox is the moment in which the plane of Earth's equator passes through the center of the Sun's disk, which occurs twice each year, around 20 March and 23 September. On an equinox, day and night are of approximately equal duration all over the planet.

They are not exactly equal, however, due to the angular size of the sun and atmospheric refraction. To avoid this ambiguity, the word equilux is sometimes (but rarely) used to mean a day in which the durations of light and darkness are equal. The word is derived from the Latin word aequinoctium, aequus (equal) and nox (genitive noctis).