No, it's the actual battery charge. When it gets to full charge, the charging system stops, and the regenerative braking is replaced with traditional disc brakes.
Like you said, storage cells can't instantly accept all that charge, or you could pull into a charging station and then leave in a few minutes...just like a fill-up.
Don't forget that a hybrid's battery is relatively small. It doesn't have the capacity of a fully electric car. For example:
The 2015 Toyota Prius plugin has a 4.4kWh battery, good for 11 miles in electric mode. It's doubled in capacity in 2017.
In contrast, the third-generation Prius (not plug-in) has a battery that is only 1.3kWh - about 1/3rd the capacity. So, if it could be locked into EV mode, it could only be driven a few miles.
My concept there (and it may already be in use, or under development) is to build a "battery" which is a combination of EV-cells (for durable charge) and a bunch of Megacapacitors (for instant charging) and probably some diodes to control current flow.
I'm actually surprised we haven't seen the use of ultra-capacitors in a hybrid, yet. Perhaps there is a safety issue with shorting them in a crash, although LiIon batteries have the same problem.
Yeah, between the caps, the hydrogen and any aluminum, the spectacle could look like the engineering section on the Starship Enterprise when they have a power surge in the flux capacitors.