Hi
The pronunciation \{foo'-sis} and {foo-see-kos'} that you mention refer to the ancient Greek and not the current pronunciation of the words.
The ending -ις in the word φύσις is an older ending as well. In modern Greek we use the ending -η (φύση). Do you study ancient or modern Greek?
Anyway, the two words come from the same root. φύσις (or φύση) is a noun and φυσικός, φυσική, φυσικό is an adjective.
φύση = nature
φυσικός = natural
Example from modern Greek:
Μου αρέσει να κάνω εκδρομές στη φύση.
Το φυσικό περιβάλλον είναι πολύ όμορφο.
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.