The PERMISSIVES, are some conditions that need to be satisfied before you can start the machine. For e.g. a compressor can be started only when there is sufficient suction pressure.
INTERLOCK: During the process, if a condition fails, interlocks are activated. For e.g. a pump shutdown interlock is activated when the level of drum goes low.
Difference between Permissive and interlock ?
An interlock can also be a permissive, but the converse is not true. For the compressor example (in Permissives), if insufficient suction pressure is a permissive, the compressor will not shutdown, if there is insufficient suction pressure. It is just a condition for the system to start.
But if insufficient suction pressure was an interlock, the system will shutdown, when ever the suction pressure goes below a fixed value. But once shutdown, all the permissives need to be satisfied before the system can start again.