I still don't understand what a cover is. Is it the cancellation stamp?
A cover is essentially an envelope (it got it's name because it covers the contents), usually stamped and those stamps cancelled.
Here's some examples of fancy covers:
https://store.usps.com/store/results/collector-s-zone-first-...
According to https://en.wikipedia.org/wiki/Event_cover
they are "decorated, stamped and canceled commemorative envelopes"
Essentially they are envelopes with stamps and a marking over the stamps that prevents the envelope and stamps to be used.
The article's talk page actually has a similar discussion over whether to call them stamps or covers in the title, so although they come down on your side its hardly a given.