Consider the sentences:
- The tone of the interview varied while one video showed the teacher acting cordial, the other hostile.
- The tone of the interview varied: while one video showed the teacher acting cordial, the other hostile.
In 1, "while" means "at the same time" or "simultaneously", and the while-clause modifies the verb "varied". "The tone of the interview varied while one video showed the teacher acting cordial" would be fine, expressing two things happening at the same time. But the full sentence is problematic because what does "the other hostile" do at the end? It is an ungrammatical fragment.
In 2 "while" is used to contrast two things: the teacher acting cordial (nice), and acting hostile. Here things are not happening at the same time: "while one video showed the teacher acting cordial, the other hostile" is a new main clause and could be a standalone sentence. Hence, because it's a separate main clause, it needs to be separated by punctuation or a conjunction.
Note that it's actually a bit unusual to use this amount of elision (omitting repeated words), which might be confusing. "While one video showed the teacher acting cordial, the other showed them hostile" or "while one video showed the teacher acting cordial, the other showed them acting hostile" would be more common and reveals the actual structure. But in formal writing, it's possible to use parallelism to remove more words.
Compare senses 1 and 2 of while as a conjunction in Merriam-Webster.