What is the opposite of synecdoche?

If synecdoche represents when a part of a thing or person refers to the whole, what is it called when the whole is used to refer to a part?

For example, we often hear about what "The American People want". Yet such claims usually refer to what a segment of the people support. What is that rhetorical device called?

Another example, "The students were devastated to hear that the beloved football coach had died." All students? Even those who did not know him? Even those who never watch football? Is this just plain old exaggeration, or is there a word for when the whole is used to refer to a part?

Synecdoche is a figure of speech in which a term for a part of something refers to the whole of something, or vice-versa. So you may use synecdoche for both. Please check

Generalisations - statements or opinions which are only partly true because they are based on a few cases or incomplete knowledge.