My understanding is the same as what you were speculating on - that it is a controlled charge. In the old days, the adapter just pumped power into the batteries, whether they needed charging or not. “Modern” adapters when paired with the matching battery bank will attempt to optimize the charge to what the battery needs to maintain a charge, provide a full-charge, or just maximize battery life.
It’s logical then to assume that you need to match the power-adapter you purchase to the device you’re charging, following the manufacturer’s specifications.