Grains are a measure of weight, used both to measure the weight of bullets and powder charges.
It's very rare for an ammunition manufacturer to advertise the powder weight, so it's safe to assume that the grain numbers refer to the bullet weight when you're buying commercial ammo.
The common bullet weights in 9mm are 115gr, 124gr, and 147gr. Generally speaking, in a given caliber, a heavier bullet will penetrate more deeply while the lighter bullet may expand a bit more and will have higher velocity.
The cost differential was not specifically related to the bullet weight, it was related to the higher quality and performance of the ammunition. It's very likely that a 115gr premium hollowpoint defense loading would cost much the same.
Premium self-defense ammo tends to be a good bit more expensive than FMJ training ammo for several reasons.
1. A misfire or jam at the range while practicing doesn't threaten your life. The extra QA that goes into making sure that doesn't happen with your defense ammo isn't free.
2. It costs money to develop a premium expanding defense round.
3. It costs more to manufacture a premium expanding defense round.
4. Self-defense ammo may employ more expensive components such as nickel plated cases or low-flash powder.
+P and +P+ refer to higher pressure than normal.
9mm is limited to 35,000psi peak pressure.
9mm +P is limited to 38,500psi peak pressure.
9mm +P+ does not have industry established pressure limits.
Generally speaking, increasing the pressure increases the velocity and probably also increases the terminal effect of the bullet although it's not clear to what extent. It also results in more recoil and will accelerate wear on the firearm although most people don't have the money to wear out a firearm by shooting +P ammo in it.
