The last highlighted sentence is a bit confusing.
It's all about optimizing the tiny details in cell manufacturing.
A manufacturer can make a so-called energy cell, which has energy density like 300Wh/kg and cost of $150/kWh. But it can be discharged at some 1C max, meaning it must be discharged during one hour or longer. Short peaks of higher current are of course acceptable.
Or, they can make a power cell, which has energy density of just 250Wh/kg and cost of $200/kWh, so it's inferior in energy storage. But it can be discharged at 4C max, meaning you can run it flat in 15 minutes; peaks even higher.
Those power cell are used in power tools like drills, and maybe in hybrid EVs because the capacity is so small yet you need quite some power in acceleration so the relative current to capacity is high.
Today's full electric vehicles are not very "high power" in this regard. If you have 250km of driving range, maybe you discharge it in two hours, i.e., 0.5C discharge rate. This is well within the capabilities of classical "energy cells". This doesn't matter though because EVs are such large business today that the battery manufacturer will micro-optimize the cells for exactly what the car manufacturer wants, so it makes no sense to group the cells in the two strict categories.
But it helps understanding the literature to know about those two classic categories, and also understand there is no large fundamental difference, just manufacturing details. At cell chemistry level, high power cells prefer to have more active surface area so that reactions can happen faster, at the expense of having less "bulk" material. The materials and chemicals might be exactly the same, or there can be some small "secret sauce" differences I have no idea about.