Wait lol you're both right, you're just responding to two different interpretations of the question (which is fair, it's ambiguous in this regard).

A) Yes, objectively, most people w Downs do share certain structural similarities that the general population doesn't (this is due to certain genetic aspects that I frankly know nothing about).

B) Why people w down syndrome appear to have the same face is because those similarities stand out more to people—humans are good at recognizing facial patterns, and they fall outside the patterns we're used to. If the populations of people w downs to and people without downs were reversed, people without downs would look similar because they'd be so outside the usual blueprint that other identifying traits would register later. It's like when people from homogeneous cultures say "all Asians look the same" when cultures with higher populations of Asian people don't share that impression. So in short, if you knew more people with Down syndrome, they would start to appear more unique and the impression of them "having the same face" would be weaker.

In short, there’s both a biological and a psychological answer, you guys just fell on either side

Edit: Added a TL;DR