I thought so as well, but we were asked for sponsorship instead of donations again and again, not because they wanted more of a service but "because I need an invoice"

It might be that the legal framework is there, but the process within companies is not. I'd be interested in someone correcting me if I misunderstood things

You know it's never something I've thought about before but if a group of students came to me looking to go to a trade show I would expect them to use the word sponsorship, whereas if a homeless shelter came looking to support their daily operations, I would expect that to be a donation.

I think the critical different is that the sponsorship is for a specific activity, but I'm not sure.

There's certainly tax structure in place for donations in the US, but perhaps there is also a custom regarding sponsorship.