The short answer: Usually 'that', but also 'which', is used to begin modifying clauses that are restrictive or defining - they are necessary to identify the referent, and they are not preceded by a comma: The girl that I marry will have to be as soft and as pink as a nursery . 'That I marry' identifies 'girl'; otherwise, we would not know which girl was being talked about. Only 'which' can be used to begin modifying clauses that are not restrictive or non-defining - they just add extra information about the referent; they are not necessary to identify it.
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