word choice - Correct usage of "which"/"that"

From what I understand the second sentence is correct, and the first is not. What are the rules on using which versus using that?

1. Instead it produces the above, which simply is a silent error.



2. Instead it produces the above, that is simply a silent error.

Answer

The notes about when to use which and that reported from the NOAD are the following:

In U.S. English, it is usually recommended that which be employed only for nonrestrictive (or nonessential) clauses: the horse, which is in the paddock, is six years old. (The which clause contains a nonessential fact, noted in passing; the horse would be six years old wherever it was.) A that clause is restrictive (or essential), as it identifies a particular thing: the horse that is in the paddock is six years old (not any horse, but the one in the paddock).

To notice that (in sentences similar to the ones you used as example) which is generally preceded by a comma, and that is generally not preceded by a comma.