At least for English, those "fansubs" aren't typically burnt into the movie*, but ride along in the video container (MP4/MKV) as subtitle streams. They can typically be extracted as SRT files (plain text with sentence level timestamps).
*Although it used to be more common for AVI files in the olden days.
I have also found them inside mkvs as the subtitle track. I think SRT was the default because most content was ripped from DVD/BD, but now most of the content is from streaming sources and you need to convert the subtitles anyway.
*Although it used to be more common for AVI files in the olden days.