That's not what people use the term "self-hosted" for. It doesn't really apply to websites that you created yourself. It rather applies to off-the-shelf software that you use as an alternative to SaaS offerings.
Perhaps we need a new term or two to distinguish between "services I provide through providers" and "services I provide with my own metal" (except ISP and power, 'cause I run my services but I'm not buying a power plant).
At the moment people, myself included, use "self-host" for both.