The word ‘ dessus’ can be an adverb ( or a masculine noun) and doesn’t belong in this classification.
It actually means on top of something :
Je t’ai déjà dit que ton porte-monnaie était sur sur la table = I already told you your wallet was on top of the table
Je t’ai déjà dit qu’il était dessus = i already told you it was on top of it
I would actually translate sur with "on": two objects which touch each other, one being "on" the other:
Le verre se trouve sur la table. -- The glass is on the table.
And, as you propose, dessus would be "on top of". "Above" (overhead) would be au-dessus. Mostly, however, dessous and dessus are used as adverbs, as in:
Voici la table. Mettez votre verre dessus. -- Here's the table. Put your glass on it ("on top").
Then there are certain combinations of dessus, like au-dessus:
Le verre se trouve sur l'étagère au-dessus de la table. -- The glass is on the shelf above the table.
Here is a nice summary: https://www.thoughtco.com/dessus-and-dessous-1368833
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