TCG means Trading Card Game. When a player purchases a pack of cards for a TCG, they do not know what cards are included in the pack as it’s randomized. Packs are typically called Booster Packs and the cards included in the pack are rated on their rarity. The Trading aspect of the name comes from players trading cards to get the one(s) they desire since the packs are randomized. TCG is sometimes known as a CCG, or Collectible Card Game. Magic the Gathering, Pokémon, and the Keyforge game are good examples of TCG’s.
LCG means Living Card Game. The term is trademarked by Fantasy Flight Games and only applies to their property. The concept is the same as a TCG with one major difference: the packs of cards are not randomized. When a player purchases a pack for a LCG, they know exactly what cards they’ll be getting. Players are on equal footing with their purchasing power whereas with a TCG, if I buy a Booster Pack and my spouse does, there’s a strong possibility one of our packs is superior to the others. Arkham Horror the Card Game, Game of Thrones the Card Game, and Netrunner are good examples of LCG’s.
Quick and to the point.