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Because they are your "own cloud" vs. the Big Tech cloud services. The meaning of words change and a person not in tech would never call something "an application server", which is perfectly fine.

Most people not in tech don't even know the word cloud in a context related to computing anyway. They know google drive/workspace, Microsoft 365, dropbox, that's it.

EDIT: OK not living in the Apple ecosystem I realize I forgot about icloud which at least in term of market shares in the USA is a big thing (but not necessarily everywhere else).

It's fairly common in the marketing materials of all of the services you mentioned. Many people also know it from when the cloud was a popular buzzword.

I thought 'the cloud' meant 'someone else's computer', but in light of personal cloud software like this, I might have to change that. 'Some other computer across a network', maybe?

https://en.wikipedia.org/wiki/Semantic_change