This the inside of Ridgid's new 18-volt Hyper Lithium battery. The type of cells that were used determine the amp-hour rating - this is a 4.0 Ah pack. Among other things, the electronics provide short-circuit protection, over-discharge protection, and over-current protection. There is nothing unusual about the amount of electronics in this pack; nowadays, most packs contain some kind of circuit board. This one just happens to be big.
... look on the other side where the rating might be printed, but that number is only shown on one of the batteries. The other way is to do some simple math based on the label...
The one thing I remember from high school physics (maybe the only thing) is that Volts x Amps = Watts. That means Volts x Amp-hours - Watt-hours. The Watt-hour (Wh) ratings are printed on these packs so you can work backwards to the Ah ratings. The pack on the left is the older 3.0 Ah pack and the one on the right the newer 4.0 Ah pack
This is the new compact Hyper Lithium battery. it has half the number of cells of the high capacity battery, which is why it's 2.0 rather than 4.0 Ah. Still, it's better than the older compact pack, which was 1.5 Ah. This size pack is what normally comes with Ridgid tools. There may be a few that come with the larger, high capacity pack, but usually they come bare or with compact packs.
This should be familar to anyone who uses sub-compact tools. It's a compact (three-cell) 12-volt (10.8-volt nominal) pack. It's the newest model and if you look at the label you'll see that it's rated for 2.0 Ah.