Aren't subtitles and closed captions the same thing?

There are two types of subtitles: for the hearing impaired and normal subtitles. English subtitles are usually for the hearing impaired, which means that they also add information about the sounds of the scene, like the phone is ringing or the music is playing.

I think closed captions include description of noises, music cues, etc.

CC subtitle tracks often show up with the name "English (SDH)" (Subtitles for the Deaf and Hard of hearing).

https://en.wikipedia.org/wiki/Closed_captioning

Thanks, I wondered what that implied. Though I don't really understand what the point of [music] would be to a deaf person.

I’m not deaf but I watch a lot of video content with no sound and only CC captions. Usually with my own music playing instead.

When the CC is good it can communicate the mood of the music that is playing, sometimes it even shows the lyrics.

[ominous music], [workout montage music], [knocking on door], [Rachel clears throat], [music: Comfortably Numb by Pink Floyd]

Usually there tends to be a description connecting the music to a specific kind of emotion, but it could also be a generic music symbol that leaves the person to imagine something in its place. Deaf people can still feel a subset of the vibrations that sound creates (usually the low end bass frequencies played with a higher power output). So a subset of such deaf people may be able to relate to certain sounds with certain emotional content too. The number of humans who cannot hear is a union of two sets – those who were born without the ability to hear and those who could hear but lost it at some point in life. The closed captioning indicators for music leave it to the imagination of the person.