Gamma vs Theta

The rate of change of delta relative to a $1 change in the underlying price; highest for at-the-money options near expiry; long options have positive gamma; short options have negative gamma; high gamma positions are unstable and require careful management near expiry.

The rate of change of an option's price relative to the passage of one day, all else equal; always negative for bought options (time decay reduces value); always positive for sold options; accelerates as expiry approaches; measured in dollars lost per day from time decay.