Is there any term for an interface in which an application runs another application? For example, one website rendering UI from other website within its frame.
A multiple document interface (MDI) is probably what you are looking for.
If you're purely looking for a term, I've heard "Portal" used in this context to describe the ability to run another application within a single client.
There are various approaches to how the applications run, which will depend on platform, as others have mentioned an iFrame is one approach, albeit not the greatest solution!
Depending on the application (how the other apps and packaged, used, and what control you have over them) it's possible to achieve this behaviour using "Micro-frontends". There are several different ways you can compose an application using this approach.