For example, in the software, one of the archetypal quads is protagonist, antagonist, skeptic, and sidekick. On the website that same quad is protagonist, antagonist, guardian, contagonist. Which one is correct?
Both and neither.The quads depend on your Objective Story Domain.
There are four different arrangements of the character archetypes, one for each of the four domains (Situation, Activity, Fixed Attitude, and Manipulation [Psychology]). Archetypes are like primary and secondary colors. Each is simple and 'pure'. However, they represent shorthand understandings of the relationships between elements from which they are made. It is always better to look at the elements than the simplistic archetypal labels.