When I arrived home, the door was locked. That meant no one was inside.
When I arrived home, the door was locked, which meant no one was inside.
Is "that" or "which" the right choice? Are the interchangeable here? Why or why not?
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You've used both of them correctly, and they mean the same. However, the different structures you indicated are necessary. "Which" and "that" can't be interchanged between the two structures.
"That", as a pronoun, not as a subordinator, can refer to something that came in a previous sentence, or to anything at all whose meaning is established.
"Which", as a relative pronoun, can head an adjunct clause referring to something in the same sentence, but can't refer to something in a previous sentence.
The two sentence constructions are different.
In the first sentence, you are using that as a simple pronoun to start a new sentence. It refers to something in the first sentence - "the door was locked".
In the second sentence, which is a relative pronoun. It starts a relative clause, which provides additional (in this case, non-essential) information about the main clause.
that can also be used to replace any wh- relative pronoun, though it is only used in defining relative clauses- ones that provide essential additional information about the main clause.
I found the book which I lost yesterday
I found the book that I lost yesterday
The relative clause defines which book we are talking about- this is essential information for the listener's understanding of the main clause.
You cannot use that in a relative clause that provides additional, non-essential (non-defining) information. In your sentences, the additional information is non-essential, so you cannot use that as a relative clause.