The Legend of Zelda: Tears of the Kingdom is the sequel to the 2017 game Breath of the Wild. We find the hero Link along with princess Zelda in a quest when they happen upon Ganon’s sealed corpse. Unbeknownst to them, malice have made its way to the sealing chamber and released Ganon from his shackles, causing Hyrule to fall into darkness once more.
To answer the question, it is highly recommended to play Breath of the Wild first before playing Tears of the Kingdom considering that Tears of the Kingdom is a direct sequel. But since it is a standalone game and not an expansion, you do not necessarily have to have a copy of Breath of the Wild on your Switch, although there might be save file bonuses that may be given for having a Breath of the Wild save file. It would still not feel right if you just start playing Tears of the Kingdom without at least having some knowledge about the events of the previous game, though.
The main difference between the two games, story-wise, is that the Great Calamity was just hindered for a bit and that the final boss that Link defeated was just Ganon’s spirit and manifestation of malice. Zelda knew of this, as shown in the true ending of Breath of the Wild, and therefore she and Link did not stop making sure that all their defenses are in place in the event that the Great Calamity does happen.
Now that Ganon has his body unshackled, he is set to bring darkness and destruction on Hyrule again. Unlike before where Calamity Ganon was sealed in the castle by Zelda, it is shown that Ganon has now made the Hyrule Castle his base, raising it up from the ground while razing most of Hyrule into ruin. It is still unclear, but the Sky Islands that are the prominent addition to the game seem to be not the work of Ganon, but rather done by something or someone as a way for inhabitants of the land to use as a refuge from the Great Calamity.
Check out this video by NintendoBlackCrisis talking about pointers in one of the latest trailers in The Legend of Zelda: Tears of the Kingdom: