Who is for people. That is for things, ideas, and groups that are not named as people. The student who finished early is right. The test that we took is right. Relative pronouns as a set are in relative pronouns.
Person or not
A named person, a teacher, a teammate, a writer: who (or whom if it is an object). A school, a score, a passage, a method: that. The coach that stayed late is the usual trap. Change it to who.
Which is a different fork
Extra information about a thing often takes which with commas. Needed information about a thing often takes that with none. That split is in which versus that. Subject versus object for people is in who versus whom. Case overall is in pronoun case.
The bottom line
If it is a person, start with who. If it is a thing, start with that.
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