ISSET checks the variable to see if it has been set, in other words, it checks to see if the variable is any value except NULL or not assigned a value. ISSET returns TRUE if the variable exists and has a value other than NULL. That means variables assigned a " ", 0, "0", or FALSE are set, and therefore are TRUE for ISSET.
EMPTY checks to see if a variable is empty. Empty is interpreted as: " " (an empty string), 0 (0 as an integer), 0.0 (0 as a float), "0" (0 as a string), NULL, FALSE, array() (an empty array), and "$var;" (a variable declared, but without a value in a class.