I'll digress from the SC examples that have been posted and try to get back to the original question: the difference between "that" and "which."
Consider a row of seven houses, some blue and some white. Let's say that this is how the houses are arranged:
blue, blue, white, white, blue, white, blue
Suppose I say, "My house is the third house, which is white." I'm referring to the third house in the row of houses. Oh, and by the way, that house happens to be white. This is called a nonrestrictive clause because the fact that the house is white is a parenthetical fact about the house. Notice the use of commas to set off this clause. It shows that this is not an essential piece of information. Similar to comments above, removing the clause does not alter the meaning.
Now suppose I say, "My house is the third house that is white." Now I'm referring to the sixth house because among the white houses, the third one is in the sixth position. There is no comma here because "that is white" is a restrictive clause: it contains essential information to modify "house" and to make it clear to which house I'm referring.
that and which
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