In my oppinion these terms refer to the content of protein in some samples (from different sources), like milk. But with a slight difference. The true protein refers to the content of proteins (which have Nitrogen of course) without taking into account the NPN (non-protein Nitrogen).
In Protein Science is more common to use "Crude Protein" refering to the total amount of protein in an extract.
The terms "crude" and "true" are not scientific terminology but a sort of slang. Generally a "crude" protein refers to a mixture of the protein in question and other proteins: meaning an impure preparation of the protein. "True" protein is not a term with which I am familiar. A protein preparation can be "pure" meaning it is homogeneous in that protein and contains no other measureable contaminating other proteins. It is possible that other different proteins are still present but at concentration levels below that can be detected with available measuring procedures.
The simplest thing to measure is the total amount of nitrogen present. Assuming that it all comes from protein gives the "crude protein" value. Assuming that some fraction comes from other substances yields "true protein". (Still not a true measure of the protein present, though. That's harder to do.) Different fractions are used for different foods.