So, within the community of ace folks, terms evolved that became known as sex stances; sex favorable, sex indifferent, sex averse, and sex repulsed. Note, these are different from sex positive or sex negative, and if you want to know more I wrote about them here. The main important ones for these two microlabels are sex repulsed and sex favorable. Apothisexual is considered another, shorter way of saying "sex repulsed asexual", i.e. not only does the person not feel any sexual attraction, but the actual concept and act of sex actively makes them feel bad in some way. The amount of ace folks who are sex repulsed is still up for debate, but the micro-label was mainly created to communicate both the sexual orientation and the person's stance towards sex for themself in one word.
Cupiosexual is a short way to say "sex favorable asexual", i.e. they don't feel any sexual attraction, but are still up for and potentially even pursue sex for other reasons than attraction. What reasons? Well, they might just like how it makes them feel, or they might want to have sex because it makes their partner happy and that makes the sex favorable ace happy, they might just enjoy is as a physical activity no different from running or some sort of sport.
These two micro-labels are less used, but I wanted to include them to show how sometimes these labels are more shorthand than anything independent of all other identifiers. And they represent two different areas of the ace community that can cause friction against each other. Note that these two aren't diametric opposites, but rather two sides of a single coin. They are most commonly used by people who feel no sexual attraction at all, who use the term asexual as their only other identifier; it's fairly rare that I've seen gray aces use these terms, and the community usually just uses the sex stances in combination with their ace identity.