Subtitles assume you can hear the phone ringing, the footsteps outside the door, or a thunderclap. Subtitles are always open. Captions are in the same language as the audio. Subtitles are a translation. Subtitles also translate onscreen type in another language, e.g., a sign tacked to a door, a computer monitor display, a newspaper headline, or opening credits.
Subtitles never mention the source language.
A film with dialogue in multiple languages will feature continuous subtitles that never indicate that the source language has changed. Captioned programs aren't subtitled after captioning. Dubbed programs can be and are captioned. Captioning, as far as they are concerned, is subtitling, while subtitling is also subtitling. National differences and history be damned.