@aburka
No, that's correct. Closed captioning is a technology invented for broadcast TV and refers to text overlaying the image you can turn on and off with your TV remote. So in online video, captioning you can turn on and off are closed captions and captions "burned" into the video itself are open captions.

I'm not familiar with the terms used by theaters but AMC calls text everyone can see on the screen "open captions," which makes sense. Whether captions on a device in a theater are always called "closed" or something else, I don't know.
@isaaclyman