Golden Sun
The Djinn system is basically a properly executed Junction system.
Each Djinn can be Set (Junctioned) to a character. Each one has its own minor stat boost that it gives a character as long as it remains Set. In addition, different types of Djinn in different combinations will change a character's class, which provides larger stat boosts.
By using a Djinn in combat, you can Unleash their unique effects, which are typically powerful attacks, healing, shielding, etcetera. But, by doing so you lose the Djinn's stat boosts and effect on your class. So the more you use, the weaker your character becomes, similar to Magic in FFVIII weakening the stats its Junctioned to as you cast it.
Unleashed Djinn go to a Standby mode. From here, you can either take a turn in combat to Set them back and regain their stat boosts (or do it for free out of combat), or use the Standby Djinn to perform a Summon (the more Djinn you have on Standby, the more powerful spirit that you can Summon). After you Summon them, they will slowly Set themselves back to the character (at a rate of 1 Djinn per turn).
So, the most basic way to use them is to Set them, Unleash them for their effects, then perform a Summon and wait for the Djinn to go through the Recovery state and Set themselves again.
It copies FFVIII's system of having powerful abilities that weaken your character, but it's a LOT better executed.
Summons are your most powerful attacks, but the more powerful a Summon is, the more Djinn it requires, and the longer it will leave your character in a weakened state (and the more prep work you have to do Unleashing Djinn to Summon in the first place). So, instead of GFs having health, they can instead be used less frequently, do more damage, and leave your characters substantially weakened both before and after using them.
Djinn are the equivalent to FFVIII's magic spells. Using them harms your stats and can change your class, which can change access to what spells you have. But, Djinn are generally powerful to make this tradeoff worthwhile, and unlike the game's spells, don't require PP, just time and stats. Some Djinn nearly double your attack strength, some can drain enemy health or heal the full party. There's even one that reduces all damage you take by 90% for one turn. Yeah, taking a stat loss for that is rough, but that is a POWERFUL effect. So while magic is nearly worthless in FFVIII, Djinn are a very worthwhile tradeoff that you have to consider when and where to use (as well as calculate when to Summon with them and take that stat loss for longer).
Finally, there are your basic attacks, which are generally your weaker options until you gain access to some of the endgame weapons. But they're very reliable and don't come with a stat penalty. And spells use PP and won't usually do enough damage to one shot enemies (especially at the beginning of the game), but can affect multiple enemies at a time, giving them their own utility.
Overall, the system is just much better balanced and executed. It serves the same idea of having powerful effects that reduce your stats, but it cuts out the entire draw/refining system in place of acquiring a much smaller number of Djinn, which each have a larger individual impact on your stats. And it makes these strong enough to actually use, instead of just taking the stat buff and forgetting that you actually have spells the way you do in FFVIII (though note, you CAN play the game without Unleashing or Summoning Djinn if you want, it's totally viable).