[Carmen]

Do I have the following right?

• A FDC is usually issued by an official postal authority, like Canada Post
  

• A Cover can be a First Day of Issue type of thing, but usually done by a private company or person (i.e. like the Roger Tory Peterson cachets I'm currently cataloguing).
  

Yes? No?

[Webmaster]

Not quite.

A First Day Cover can be any cover, philatelicly created or even commercial in nature, that is cancelled on the first day of issue of the stamp. It is frequently further described to differentiate the types, as in: Canada Post Official FDC, FDC with private cachet, or even "commercial use FDC". It may be cacheted, uncacheted, with or without the official FDC cancellation (i.e. Ottawa First Day of Issue) if one even exists.

A "cover" is basically any item that went through the mails. 

Roy