Despite their seeming similarity, captioning and subtitling have very little in common. The assumed audience for subtitling is hearing people who do not understand the language of dialogue. Captions notate sound effects and other dramatically significant audio. 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.