While going through the 2015 upgrade audit, our CB suggested we change everything to the new terms to "clear things up". I refused and he wasn't happy. But then again, this was a witness audit by ANAB so he was a bit more nit picky. That being said, I was not impressed by the ANAB auditor, who spent most of his day online shopping and playing games on Google.
We don't use "suppliers" or "external parties" - we use "vendors", lol.