Yes, they are very different names.

But Italian immigrants named Vincenzo who came to the US (or were born in the US) commonly use the name James or Jimmy in their daily life. No one knows why, other than the possible similar sound of "cenz" and "James".
Carmine

My hobby is finding things. Having ...

I always thought that Vincenzo = Vincent and James = Giacomo. Is that wrong?"
is correct - two different names:

JAMES
GENDER: Masculine
USAGE: English, Biblical
PRONOUNCED: JAYMZ (English)
VARIANT: Jaymes (English)
DIMINUTIVES: Jim, Jem, Jay, Jamey (English)
OTHER LANGUAGES: Yakub, Yaqub (Arabic ...