The Pilot/Controller Glossary only has one instance of "no delay":
Indicates that an aircraft’s fuel supply has reached a state where, upon reaching the destination, it can accept little or no delay. This is not
an emergency situation but merely indicates an emergency situation is possible should any undue delay occur.
"Immediate takeoff" doesn't exist, either, but we do get
IMMEDIATELY − Used by ATC or pilots when such action compliance is required to avoid an imminent situation.
We can cross-reference this with the Skybrary entry for Immediate Takeoff:
When given the instruction ‘cleared for immediate takeoff’, the pilot is expected to act as follows:
- At the holding point: taxi immediately on to the runway and begin a rolling take off without stopping the aircraft. If it is not possible to begin taxiing onto the runway at once or if take off performance calculations mean that a standing start is necessary, then the clearance must be declined
- If already lined-up on the runway: commence take-off without any delay. If this is not possible for any reason, the pilot must advise the controller immediately.
So that suggests that "immediate takeoff" is more standard. My experience has always had the clearance be "no delays".
If the P/CG doesn't technically define either phrase then I can suppose that they use "no delays" to avoid the knee-jerk "I must do something" to "immediately". For "no delays" you can always easily respond "unable" and wait until the next plane lands.