Standing Wave: When interfering waves, have the same amplitude and wavelength, the resultant interference pattern remains nearly stationary and is called as standing wave interference pattern, a nodal point is a point that remains at rest throughout the interference of the pulses.

Deconstructive Wave: When a crest and trough meet “the waves are out of phase” the energies combine work against each other – they tend to cancel out.

Constructive Wave: When a crest from one source meets a crest from another source, the energies combine to displace the medium (energies are the additive), same thing occurs when trough meets trough.

How do noise canceling headphones use wave interference to eliminate unwanted sound?

The noise cancelling headphones transmit equal but opposite wavelengths which cancels out the sound/noise just like how deconstructive waves work.