The difference between noch and mehr can easily be explained, but it requires some practice to fully get used to it.
Have a look at these 2 sentences, for example:
Möchtest du noch Kuchen?
Möchtest du mehr Kuchen?
In this context, they mean essentially the same: Do you want (some) more cake?
The situation gets even more confusing, when you know that there is also the expression lit.: still morenoch mehr :
Möchtest du noch mehr Kuchen?
The important difference to remember, however, is that "mehr" translates as "more" and "noch" translates as "yet" or "still". In English, we would usually not say "Do you still want cake?". In German, it's totally fine to phrase it like that. And in these example sentences, mehr & noch are pretty much equivalent.
However, the implication with "noch" is often that something isn't really completed yet.
Imagine you're having some cake at your friends house and your friend then asks you "Möchtest du noch etwas Kuchen?".
What's often implied here is that your friend will put the Kuchen away, if you say no. He wants to "complete" the activity of "eating cake together", if that makes sense.
Or consider this: