Are there specific musical terms describing time structure like 4 bar sections, 8 bar sections, 16 etc.?
1 Answer
You would just refer to it as a section, if it is a complete section, or by the name of the section if you are trying to communicate the part of the song.
For example, "take it from the bridge" (sometimes called the "middle 8" or "middle 16") or "take it from the 4 bars before the 2nd chorus". Jazz musicians might call the main part of the song the "head".
Someone might refer to a small section of a song by the word "passage".
But in general if you are not referring to a specific section of a song you can say the first 8, 16, 32, bars starting from x.
In a band setting you are almost always going to refer to a named section of the song and if you don't want to start at the top of that section you would say x bars before or after that section starts.
In a orchestral setting you will have section markings as well as bar markings. So rehearsal marking B or bar 112.