When I purchase the standard edition of a game and later I purchase the deluxe edition. Do they appear as two separate games in my collection or the same game is improved? TIA.

Usually, the deluxe edition is nothing more than the standard edition + DLC.
One exception is Witcher 3 GOTY, which takes a separate library slot.

They are one game in your collection, you should only have more files to download.

Note that GOG's website doesn't track your purchases very logically. For instance, if you buy the standard version and upgrade, you can still see the deluxe version as not owned when you are browsing the catalogue. There's really nothing you can do about that, but the downloads should be the same whether you buy base game + upgrade, or deluxe version.

Thank you for your answers I can now make an informed decision.

Just make sure there is an upgrade path available. Sometimes there isn't a catalogue entry for DLC that'll upgrade your version.

Thank you. As I see things it is better to wait until I can purchase the full version. Buying upgradable versions smells to problems.