Also, piper = the plant and the fruit from which the pepper spice is made!
Piper = pepper, the spice, ardei = pepper the vegetable. (Try a google image search on the Romanian words and you'll see corresponding images)
Accordingly to Wiktionary, both translations (pepper as the spice, and the plant) are correct.
From Slavic piperĭ, Greek πιπέρι (pipéri), from Ancient Greek πέπερι (péperi).
1) pepper (plant)
2) pepper (spice)
From Wiktionary: https://en.wiktionary.org/wiki/piper