This is all essentially correct. I just want to clarify a few things. (Not to you WF, to the others, I'm just using your post to do it) Typically the larger wires are referred to as the "main lead" and the smaller one is called a balance lead. There are multiple different types of balance leads although the "JST-XH" is by far the most common connector. Besides JST-XH there are also JST-EH, Thunder Power (TP), Hyperion, and Polyquest connectors. Hyperion and Polyquest are interchangeable though. I dont know how things are these days because the last time I bought a Thunder Power or Hyperion charger/battery was probably close to a decade and a half ago but TP used to come with TP connectors and Hyperion used to come with hyperion connectors. Just FYI.
LiPo chargers are called "Constant Current Constant Volatge", or CCCV chargers. They are called that because thats how they operate as WF explained here. The first phase gives the battery constant current for 70-80% of the charge and then once the LiPo reaches a point where that constant current would be to much and overcharge one or more of the cells it goes in to constant voltage phase where the charger supplies the exact amount of current needed to maintain the maximum voltage of the pack. Either 4.2V or 4.35V for regular and high voltage lipos respectively. While its feeding the now fluctuating current to the battery via the main leads in the CV phase, the charger is also simultaniously pulling the over charge from cells out through the balance leads in order to ensure that no one cells goes over its max charge level. This is why chosing a charger that has the highest current possible is beneficial to speeding up the charging procedure.