Here's the thing about Mystics: most of their stats never go up. That 28 Strength Ildon has is going to be a 28 Strength for the rest of the game. They can gain HP, WP, JP, and Charm, but their Strength through Vitality stats don't increase after battle.
However, the Mystic = vampire metaphor still rings true: Mystics absorb powers from the monsters they fight.
Each Mystic starts with a MysticSword, and as they develop, learn the skills MysticGlove and MysticBoots as well. When these are used against monsters, the Mystic has a chance of sucking the monster into their equipment. This always gives a stat boost and a special skill. For example, Ildon has a LivingLance absorbed into his MysticSword, giving him +8 to Strength, Quickness, Will, and Vitality. In battle, it lets him use the ability Lance.
While the stat boosts are the same across Mystic equipment, monsters give different skills if they are absorbed into different pieces. The LivingLance gives Ildon Lance because it's in his MysticSword. In his MysticGlove, it would give Feeler. In his MysticBoots, it would give Sweep.
Ildon starts with LivingLance, Battlefly, and Armorpilla absorbed into his Sword, Glove, and Boots respectively. White Rose's stats have fewer pluses than Ildon's because she only has MysticSword, and has no monsters absorbed in it yet. (The +5 to White Rose's Psychic and Charm comes from the FlowerAmulet she has equipped.)
Mystics cannot learn sword, martial arts, or gun techniques, although they can still slash, punch, and shoot if they have the requisite equipment. Mystics do not spark skills. They can develop magic if they have the Gift for it... but the staid, unchanging, ageless nature of Mystics takes its toll: they all have the goose-egg magic-development talents of Emelia.