This is one of those "it depends" answers. Based on my experience growing up in-part in America, with other Americans, going to camp:
Size matters. Very big camps end up breaking people out in small groups, and the small groups (and entire large group) may not have award ceremonies.
Setting matters. Is this a day camp or a sleep-away camp? How long have campers attended? What age are campers? What activities do they do? How diverse are camper demographics?
These sorts of things shape the ceremony, including whether or not parents attend. In my experiences, parents are not invited during the ceremony - aside from maybe one specified visiting day and drop-off/pick-up day, and phone or mail contact as needed, parents let kids stay at camp on their own to gain some sense of independence there.
Ultimately I think we can make an educated guess that all summer camps end with a ceremony. The ritual or wrapping things up, providing closure with some reflection on past and a look to the future, is common for these sorts of things. It defines an ending point which is logistically and emotionally important.
Are these ceremonies all award ceremonies? To answer that question - definitely not. Award ceremonies can facilitate a closure ceremony, and add a fun dynamic to the reflection. Awards also give something for campers incentive to strive toward during their time at camp if they know it is coming. There are other ceremonies camps use to wrap things up however, and those as well as award ceremonies all differ from place to place (each camp developing its own unique style and subculture).