I think is just her not wanting to be specific, I don't think we should consider the deeper meaning of being equals and whatnot, seems like something said casually, that is all.

I feel like calling him her partner connects them more on a level of cooperation. Saying 'partner' insinuates that they work together well, whether it be in love or communication or both. Work partners are people who work together to get things done for their company, and school partners are people who do projects together and get them done. Your partner in life, or love, is someone who you work with for everyday things and eternal happiness, and someone you're close enough with to include them in every process or production of your world.
Calling someone your boyfriend just means you're in a relationship, and a fiancé is someone you wanna spend the rest of your life with. A partner is someone who involves themselves fully with you and your entity.
I hope this helps. Oh, and this is all my opinion on the different terms, it has no true validity.

To me (even though I'm a guy), "partner" signifies "equal". Like "business partner".
Or it could be the generic catch-all term. "Partner" can be used instead of boyfriend, girlfriend, fiance, husband AND wife. So it's easier to remember that one term.
But I prefer my reasoning. My partner is my equal. She would actually be my partner, not just my girlfriend / fiance / wife.

Maybe that she isn't all that committed into the relationship yet. Like they are just partners and might be dating a bit, but are not fully a couple. Then again, some people just have different names to call their significant others.

That they're their partner, eh? It's just genderneutral. It could be male, female or non-binary.
But I don't think it's anything different. You could be dating, engaged or married - partner is partner. Just not gendered. uwu

Idk tbh I'd have guessed only same couples would call their other half partner like I'd probably do in front of others when I talk about my gf xD