In video gaming, the HUD (head-up display) or Status Bar is the method
by which information is visually relayed to the player as part of a
game's user interface.The HUD is frequently used to simultaneously display several pieces of
information including the main character's health, items, and an
indication of game progression (such as score or level).
I assume menus aren't part of the HUD.
What's the difference?
Best Answer
UI (User Interface)
HUD (Head-Up Display)
Verdict
Looking at these definitions, the HUD is actually a part of the UI as it can have an effect on how the player interacts with the game.
For example, the Overwatch HUD which displays when an ultimate is ready to use:
Summary
When looking at the definitions and examples of how the HUD can impact the UI, it seems as though there is no right or wrong answer, as the phrases and the uses they hold in game, support each other.
Neither word should be used over the other, as they work together.
(I apologize if this answer is hard to understand, I tried to explain it as best as I could)