Bring your own server
This is a term I'm exploring around software that installs on your own server, that then fully manages it and offers other capabilities around it.
Cloudron and Coolify are two examples of this.
Another trend I'm seeing in more commercial cloud platforms is that the high end / enterprise option includes the options to plug in your own AWS or other cloud credentials. The service becomes a sort of managed PaaS, where you pay for the management and support, but separately pay AWS or other cloud provider for the data, compute, and other commodity resources used.
Fission's Everywhere Computer is also designed with the ability to always bring your own server.
Self Hosting Packages
Maybe not quite the same category, these are packages that often take over an entire server in order to install apps and manage the entire operating system.