I'd argue that HUDs are graphical user interfaces: they're ways to present information back to the user graphically.
In contrast to what some other answers say, the term GUI doesn't require that every element be directly interactive - the label next to a control on a form is still part of the GUI, guiding the player in how to interact with the system, even if clicking the label itself doesn't accomplish anything.
What distinguishes HUD elements is the particular way this information is displayed to the user: "Heads-Up Display" was coined in contrast to a light or dial on a control panel, where the user would need to look down / away from the window and world in front of them to check on it. The defining feature of being "Heads-Up" is that the information is overlaid over the world, rather than in its own separate dashboard, and it often tracks with the user's camera or head rather than needing them to turn to a particular location to see it (particularly notable in VR games).
So for example, in this StarCraft screenshot, I would argue that the selection and health overlays on the units, and resource counters in the corner, all constitute HUD, being overlaid on the game world. The map, order buttons, and selection readouts in the chrome below would not be HUD because they exist outside the world viewport.
It's more common to see the term HUD applied in 1st person and 3rd person over-the-shoulder perspectives than to top-down/isometric games like this one, but I wanted to find an example that would contrast both styles. First person examples with both HUD and non-HUD chrome are harder to find, but old-school dungeon crawlers sometimes use this kind of mix too. Here the "Small Cave Troll" label, level, and health bar are HUD since they're overlaid on the world, while the rest of the GUI sits (mostly) outside the player's window to the world and isn't "heads-up" in this sense.
Some games will also have floating windows or panels, like inventory management interfaces, that sit on top of the viewport. When these are mostly opaque, I'd generally consider them to be non-HUD GUI elements because they obscure a sizeable chunk of the game world in much the same way as the dashboard chrome examples.