HandBrake

In some movies there are multiple languages, ie: Elysium has some parts not in English. When you watch the movie just those non-English parts have subtitles but the subtitles aren't on for the rest of the movie. Or in Avengers, there is a part in Russian that has English subtitles.

First question, what is that partial subtitling called?

Second question, how do I get that? I can subtitle the entire movie in English but not just that portion.

You are asking about "forced" subtitles, also sometimes called "signs only". Most often (but not always), these are found in a separate subtitle track, but they may be mixed with all other subtitles in a single track, but be marked as "forced".

Whether or not it works is dependent upon how the disk was authored. I recommend you view the title in something like VLC, where you can manually select each subtitle track and see if it is a "full" or "forced only" track. When they are separate like this, you just need to select the "forced only" track for inclusion in the final file.

If there is only one subtitle track AND the forced subtitles are marked properly, there is a parameter for each subtitle track in Handbrake to only use the ones marked as "forced".