motion distance-time graph

It has been a while since I have touched on physics, but reading the material presented in my course, I recall displacement and distance being two different things. Distance is the total length something travels from A to B and back to A, whereas displacement would be 0 when returning to its origin.

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are

From https://en.wikipedia.org/wiki/Distance
Although this isn't quite as informative as displacement, it is still consistent with the graph given.
If they said "distance travelled" I feel you'd have more of a case.
I know there seems to be a recent trend to insist it should be displacement, but
https://trends.google.com/trends/explore?q=%22distance%20time%20graph%22,%22displacement%20time%20graph%22
indicates distance/time is still the most common terminology. [And in particular, from other things you've posted about your course, I'm guessing it will tend to use older terminolgy].

I see. So, distance/time is becoming more used in text books for teachings rather than displacement/time?
Moreover, what is more confusing is that it talks about distance/time graph but then jumps to velocity/time graph.
It’s going from a scalar quantity graph to a vector quantity graph.
So, it’s stating that I find velocity from the distance/time graph, referring to the gradient but as I recall this is only true to a displacement/time graph.
If we’re talking distance/time, we’d be considering speed and not velocity.
Also, the area under the line on the velocity/time graph, I recall being displacement but they’re referring it as distance?
My textbook teaching from Cambridge are contradicting this course material.

You seem to be overthinking it a bit in this case. Distance from the origin (a point) is different from distance travelled and the former is the same as displacement when displacement is not negative (your scalar/vector distinction and you have to choose your positive direction for the later), which is the case here. As Dfranklin notes, they have been frequently interchanged and I wouldnt say that either are more/less commonly used these days, just that distance a more familiar term than displacement. In certain cases, distinguishing between them is important, but not here.
Note that if there was a second "bump" after the first one, then youd not be able to say whether it was in the same direction as the first one, though if the y axis was displacement then youd be able to determine that.
Mixing speed and velocity here may be more problematic as the speed of the last section would be 5m/s (say), but the velocity would be -5m/s (with the usual reason about which direction is positive). However, for simple trajectories inferring that displacement is the same as distance from the origin and hence using that to determine velocity is common ... for simple trajectories.

I see.
I’m more familiar with displacement when dealing with suvat and that’s likely why I’m a little confused.
In the case that the velocity time graph had a curve though, the use of distance=speed x time would no longer apply here like they suggest to use but as their example shows steady acceleration, what they’re saying isn’t technically wrong.

I see. So, distance/time is becoming more used in textbooks for teachings rather than displacement/time?

No, the opposite. When I was at school/university, I'd say "distance/time" was far more common usage than displacement.
If I'm honest, I find the distinctions fairly pointless pedantry. If I say a rocket is traveling at a speed of -10m/s, everyone knows what that means. (Or at least they are no more confused than if I say it's traveling at a velocity of -10m/s). Similarly for distance. This seems particularly so when you're saying things like "velocity is a vector, speed is a scalar", but your handling of the problem means you're treating velocity as a one dimensional quantity. In real problems, you're far more likely to get bitten by that than by confusions about what a negative speed or distance means.

I understand what you mean. I would have considered velocity and speed as interchangeable in reality. But as I’m still learning the mechanics side of it, when I learn velocity as being different to speed and same with distance and displacement, it leaves me with questions, more than answers when I see them used as the same within a context and extremely confused.