TLDR: One is identifying as a different gender, one is identifying with a different animal.

It’s in the same paragraph you quoted:

First, reports of this phenomenon (called therians) is greatly exaggerated. They are often conflated with other groups (like furries). This is pretty clearly a social and psychological phenomenon, not a neurological trait, and having nothing to do with a system of neurological development (influenced by hormones, for example).

To the best of our knowledge, hormones don’t influence the animals you like or identify with.

From another source: https://theconversation.com/what-are-furries-debunking-myths-about-kids-identifying-as-animals-and-litter-boxes-in-schools-193908

Furries don’t identify as animals; they identify with animals. In the same way that cosplayers typically don’t believe they are actually Spiderman, furries don’t think they are their fursonas.

Is furry an orientation? It’s not. It’s a fandom. However, it’s worth noting there are many marginalized statuses within the furry community. Depending on the study, we find more than 70 per cent of furries identify as LGBTQ+ and more than 25 per cent are gender-identity diverse.