When you say "game UI", most people think of the HUD (heads-up display) that appears in front of all the in-game items. However, there are actually four different types of game interfaces: non-diegetic, diegetic, meta, and spatial.
Fagerholt and Lorentzon first described these four different interface types in the 2009 Beyond the HUD: User Interfaces for Increased Player Immersion in FPS Games: Master of Science Thesis. Since then, the terminology has been widely used throughout the field of UI game design. You can find the original publication at http://publications.lib.chalmers.se/records/fulltext/111921.pdf.
The distinction between the four is determined by a cross of the following two dimensions:
- Diegesis: ...