Ch2, p4 explains skill rank. Ch3, p5 explains major and minor skill relationships. It basically goes like this:
All major skills (with the exception of Magic) such as Archery, Swordsmanship, Summoning, Spearmanship, Shieldsmanship, etc. have 9 minor skills. They are: Pawn (Infantry), Spear (Lance), Knight, Silver General, Gold General, Bishop, Castle (Rook), Promoted Bishop (Dragon Horse), and Promoted Rook (Dragon King).
With the exception of Promoted Bishop and Promoted Rook, I don't think any of the other 7 minor skills are necessarily considered weaker or stronger than one another. They just have different acquisition methods and use cases. For example, Bishop Archery is a powerful pierce strike whereas Gold General Archery is a spread shot that does knockback (ch6, p2).
Each minor skill can be leveled up with experience from 16th Class to 1st Class, then from 1st Grade to 9th Grade. Promoted Bishop and Promoted Rook require much more experience as you continue leveling them than the other 7 minor skills (ch58, p11).
As for Magic, there are 5 elements: Fire, Water, Wind, Earth, and Lightning. Lightning probably didn't exist in the original Mobion, but was unlocked for the MC as a result of summoning the Spirit King since he's an existence that rules over the 4 other types of elemental spirits. Each element has 5 forms: Opo-opo, Raptor, Coeurl, Fourth Form, and Fifth Form (ch3, p6). Each type follows the same leveling system as other skills going from 16st Class to 1st Class, then from 1st Grade to 9th Grade. I believe unlike the other major skills, Magic's elemental forms actually do get stronger as you move up from Opo-opo to Fifth Form, but each still have use cases such as shorter cast times as seen in duels.