Closed captioning (CC) and subtitling are both processes of displaying text on a television, video screen, or other visual display to provide additional or interpretive
information. Basically, both are the same. But looking into it technically, CC offers more.
From Wikipedia article on Closed Captioning:
HTML5 defines subtitles as a "transcription or translation of the dialogue ... when sound is available but not understood" by the viewer (for example, dialogue in a foreign language)
captions as a "transcription or translation of the dialogue, sound effects, relevant musical cues, and other relevant audio information ... when sound is unavailable or not clearly audible" (for example, when audio is muted or the viewer is hearing impaired).
To put it in simple words, subtitles display the dialogue whereas CC is meant to replace sound, not just dialogue.
About your question, in most cases, the CC differs very much from the subtitles. This is because, in this case, Netflix, not only focuses on what's being said, but also on pretty much everything thats going on around. Subtitles, like you mentioned in your question, are often DVD localisations. But the CC available on Netflix could be
- made by the employees.
- made by Audio Recognition softwares.
- submitted by users or volunteers.
Therefore it leaves a significant margin for error. Hence resulting in the obvious difference between the subtitles and CC. I dont use Netflix, but it seems the matter is not exclusive to Funimation series.
And the color of the texts, I guess is just to imply that subtitles will be yellow colored while CC white.