There are more detailed descriptions on the web, but here’s a summary:
Panels go to a combiner box and then down to the charge controller. The controller adjusts the voltage from the panels to the batteries for optimum charging (as mentioned previously, optimum charging for Lithium is different than for lead acid so you need a charge controller that can handle lithium batteries). Ideally, you will have a shunt based battery monitor that actually measures amp-hours into and out of the batteries. The monitor and the charge controller work together to provide optimum battery charging. In my system, you program battery amp-hour capacity and battery type into the monitor.
Since all the loads and sources go through the shunt and are monitored by the battery monitor, it doesn’t matter if you are charging with the panels or with the on board converter/charger, all the amp-hours are accounted for.