What is the difference between a sidereal year and a tropical year? How is each calculated?

Every six months, approximately, we have two equinox instants: the Vernal Equinox and the Autumnal Equinox. The Vernal Equinox year is roughly from March 21 to March 20, which is a tropical year with 365.2421871 days, and a slightly longer sidereal year with 365.2563630 days.

At noon on the equinox, the Sun is directly overhead at a certain equator longitude.

The equinox instant is subject to annual precession, which causes it to change by approximately 20 m 23 s. The rate of angular precession is (360/25800) deg/year, or 50"/year, roughly.

The Earth's spin-axis rotates through 360 degrees in an equinox, which is equivalent to a great year lasting roughly 280 centuries.

The seasons are related to the tropical year.

Instead, we can define the tropical year in terms of a solstice. Several terms from astronomy are used here; for further information on each, see wiki.

The duration of a sidereal year, which is measured in terms of Earth's orbit around the fixed stars, is approximately 365.25636 days. On the other hand, a tropical year is measured in terms of the Sun's return to the same position in the sky, which is approximately 365.24219 days. The tropical year is determined by the Sun's position in the sky with respect to the vernal equinox, while the sidereal year is determined by the Earth's orbit around distant stars.