It has to do with analog TV & tape-based media distribution.

Captions follow a very specific standard & are required to be included on certain broadcast media.

To ensure captioning remains consistent across consumer devices, captions come in specific file formats, typically generated by a third party.

The files are delivered alongside media deliveries & contain timecode markers to sync the text up with the dialogue.

Before digital delivery of media for broadcast, each piece of media arrived on a tape. Each tape had the caption file embedded as lines of video, TVs could scan those lines as they came across in the broadcast signal, & display the captions.

On certain old televisions, you could see the captioning during the broadcast, it would appear as broken black/white dashes across the top of the image.

Any text included in a caption file is considered captioning. Any text outside of that file that appeared over video (including titles, alternate language translations, logos, etc), is considered a subtitle.

They used to be transmitted over a hidden portion of the screen, during the NTSC and PAL era. That was topologically on the signal stream area corresponding to right under the video frame. Thus they were titles (text) that were under (sub) the image. They were also unavailable (closed) to the user until they activated them, when the decoder started drawing them over the frame by folding the signal so the text could appear. They originally were invented for and proposed to aid hearing impaired people by capturing the sound events, including speech, with short descriptive texts (captioning) .

That's why in the US Closed Captioning is for hard hearing, and subtitling usually means only dialogue and other languages. While the rest of the world only uses variations of the word subtitling because English rapes and coopts everything it colonizes.