When you add liquidity, you deposit assets into a pool to support trading on a decentralized exchange. In return, you receive proof of your position, usually LP tokens or another on-chain object.
When you remove liquidity, you return that position to the protocol and receive back your share of the pooled assets, plus any fees earned by the position, depending on the pool mechanics.
Add liquidity = deposit assets into the pool
Hold LP position = own a share of the pool
Remove liquidity = withdraw your share back to your wallet