Both items noted, and anyone would be well served to cite either one as support for the term "captured". These terms (surrender and capture) are often used interchangably. The difference in interpretation is a personal preference to describe what actually happened. When a commanding officer seeks and receives terms for cessation of hostilities, that (according to my own definition) is a surrender. Commanding officers at Fort Donelson TN, Port Hudson LA and Vicksburg MS decided to surrender their garrisons.

In contast, when a soldier is overwhelmed in a combat situation and stops fighting to preserve his life, that (also according to my own definition) is a capture. For example officers and men who were taken in battle at Champion Hill MS or Gettysburg PA were not surrendered by their commanding officers. Of course you're well aware of the differences. The outline has been presented here for the benefit of those who may not understand.