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"are they provided by each network or does the cable company/satellite broadcaster make the captions?"
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Most of the time, third-party companies do captioning work for network and syndication programming: Vitac, WGBH Media Access Group, National Captioning Institute, Captionmax, etc. The company doing the transcription will usually credit themselves in a couple of lines during the show's theme song or ending credits, along with (sometimes) a copywrong date.
About the only thing the cable companies do is take peoples' grocery money in exchange for several hundreds of channels of advertising and other crap most probably won't ever watch, let alone even know it's on the system.
Quote:
"Aren't the white ones the ones where some software hears the voices and approximates it, often with misspellings?"
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Yes, as are regular human-transcribed captions. Colouration is (usually) not a reliable indication of the means by which the transcription was done. I think it's usually the transcriber's preference and varies between companies.
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"If it's a live program, obviously it has to be automated."
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Sometimes, but not necessarily. Lots of times (and all the time before speech-to-text software became viable) live programming is transcribed in real-time by a human stenotype operator. Think of a court reporter sitting in a TV studio with headphones on and a monitor before them, or sometimes actually in the studio itself, out of view of the camera. This method is slowly being displaced by computer-based speech-to-text transcription, mostly because companies don't have to pay a computer a living wage.