Same-language subtitles, closed captions, open captions, CC, SDH could all be used as synonymns in certain contexts.
Each of those synonyms have their own meaning and context so be careful to understand the difference! SDH, or Subtitles for the Deaf and Hard of Hearing, are specifically created for people with hearing disabilities. They are subtitles created in the same language as the video which also capture other plot-relevant sounds like a doorbell, phone ringtone, or offscreen footsteps.
On some video players, the user interface has a CC button which opens the subtitles menu. On YouTube, for example, you can click the CC button and see all of the available subtitle options. So the CC button can show you closed captions or closed subtitles in translated languages, but that might have been too hard to fit all of that on a little button!