I think, and it's been a while since I've played it so I could probably pop it in a bit when I'm finished up with something else, SP accumulates every time you fight battles. When you exit out of dungeons, it depletes so you need to fight battles to get it back up again. You can raise SP gain by partnering them with a character who does that. I've noticed that Neptune's SP/AP gain rate isn't as good as some of the other characters so you kind of have to tinker with her combos a little to get her to complete one.
When she levels up more, she's able to combo more, but you're noticing the discrepancy between her and Nisa because Nisa's fast, her combos cost less AP, and she builds up SP really fast. I wouldn't be surprised if people kept her in their parties just because of that alone.
AP's more complicated.
So if you don't attack, you'll gain 25% of the total AP per turn you don't attack.
If you use a symbol attack, you'll gain 50% more AP to add to your original AP.
If you attack, the calculation is basically: (AP * 0.17) + start AP while attacking.
So if Nepgear has 100 AP, and doesn't attack, she'll gain 25 AP at the end of the turn, leading to a total of 125.
If you hit an enemy on the field and got a PE Strike, you'll get your AP increased to 150 on the first turn.
If Nepgear executes three attacks that are worth 12, 14, 16, then the AP calculation is like this: (100 - 12 - 14 - 16 = 58 AP), and if you have her stand by, the AP saved will be about 0.17 of that number.