but are these parts designed to drop a frequency of a pulse, say the output of a 555, high / low pulse, or more significantly, put a delay in the running structure, e.g., turn on an led, delay pauses 400ms and then the led lights up?
delay lines are commonly used in video circuits in TV/video systems ( probably many other places that I am not familiar with)
Most TV/video circuit delay lines I have had anything to do with most often use a slab of quartz crystal rather than an inductor as shown in your circuit
can you show more of the circuit and tell us what the circuit is ?
The old Apple computer clones and boards used delay lines. I think they were essentially inductors with very high interwinding capacitance, the reason for the symbol they use. Yes that would be 400 nS. You can't get very long delays; They were just for digital signal delays.