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I would call both selfhosting.

It counts. My discriminator is the self- part. Server location is not relevant.

With the caveat that your VPS provider can access all your data should they choose to.

Both. Selfhosting is a spectrum between renting a cheap VPS and running a small data center at home (see r/homelab for the latter)

I agree, both could be considered 'selfhosting'. But in my case I am running on hardware in my house!