I see both sides. While "self hosting" has always meant hosting yourself, and hosting on other people's systems isn't hosting something yourself, I can see how people can get confused and can call running their self-configured software on a rented VM "self hosting".
It's not as unambiguously incorrect as other silly things people say and do that are technically incorrect, but it is annoying when people don't provide enough context where it matters.
Honestly, the distinction only really matters when discussing privacy. Hosting your own stuff in a rented VM is still self hosting, but if you're talking about how you self host because you care about the security of your data, you're now definitely not talking about rented VMs.
Generally, I think we need to get used to the idea that "self hosting" now also refers to hosting software you configure on rented systems / VMs.
It's not as unambiguously incorrect as other silly things people say and do that are technically incorrect, but it is annoying when people don't provide enough context where it matters.
Honestly, the distinction only really matters when discussing privacy. Hosting your own stuff in a rented VM is still self hosting, but if you're talking about how you self host because you care about the security of your data, you're now definitely not talking about rented VMs.
Generally, I think we need to get used to the idea that "self hosting" now also refers to hosting software you configure on rented systems / VMs.