As others have mentioned, VPSes (and rented dedicated servers) count as self-hosted. In many situations, a VPS can make more sense than a home server:
Better internet connection - a lot of hosts have 40Gbps connections now, and it’s a data center grade connection with a lower contention ratio.
Cheaper upfront - no initial purchase cost.
Depending on electricity prices, it can be cheaper over the long run too, especially with a $20-40/year one (see LowEndTalk, GreenCloudVPS Budget KVM, RackNerd specials, etc). That’s the case for me in California - just the electricity for my home server costs more than some of my VPSes.
Usually better hardware than you’d have at home - often AMD EPYC or modern Xeons (not a 10 year old E3 or E5), enterprise NVMe SSDs, etc.
As others have mentioned, VPSes (and rented dedicated servers) count as self-hosted. In many situations, a VPS can make more sense than a home server:
Definitely, just was unsure if self hosting means doing the hosting yourself or hosting for yourself, if that makes sense, if its either or thats nice
Discussions about hosting on your hardware is more likely to be discussed as “homelab”.