Too Long; Didn't Read
Both liquidity provisioning and yield farming generate income, but one is paid out as fees based on trades. The other is a reward given by the trading platform in exchange for locking (or “staking”) your liquidity with them. You can think of LP and farms as nesting dolls for your tokens, which let you double-dip on your investment. On ElkDex, you are actually earning ELK tokens in two ways: as fees (given along with an equal amount of the paired token) and as farming rewards.