Wikipedia definitions:
Esotericism designates all the secret teachings reserved for initiates.
Exotericism is what is public, profane, as opposed to what is initiatory. It was also used to describe public ceremonies (religious, ritual) in their manifestations. He is opposed to the esotericism which describes them in their meaning.
There is also mesotericism, which is the intermediate stage between esotericism and exotericism.
Esotericism brings together everything that is hidden, reserved for those who have the eyes to see. Exotericism brings together everything that is visible and official, for everyone.
Esotericism is the essence, the principle, the cause, the signified.
Exotericism is the substance, the manifestation, the effect, the signifier.
The two are opposite and complementary, like bark and sap. For esotericism to cross centuries and societies, it needs a supporting external structure. The visible outer layer protects and preserves secret content. The visible and objective outward manifestation reveals the underlying principles that create it. The exterior makes visible and reveals the interior. The interior enlivens and structures the exterior.
Esotericism without exotericism would be like ethereal principles which could not have manifested, like laws impossible to (re)recognize because they would remain purely theoretical. Exotericism without esotericism would be like an empty shell, a building whose walls would not be load-bearing. The two are therefore opposed and complementary, they equally need each other to exist and continue.
But esotericism contains the principles and laws linked to eternity and infinity, all of which crosses eras and cycles. Exotericism is the manifestation of these laws in time and space, lasting for a period and a cycle. Temporal and temporary constructions vary according to the eras, but their invisible principles remain the same. Esotericism should not change because its laws are immutable. Exotericism should not persist because the bricks on which it is built are fickle.