Review ASTM A 751 or ASME SA 751, if you have access. If not, the explanation below for heat analysis and product analysis are excerpts from SA 751 SPECIFICATION FOR TEST METHODS, PRACTICES, AND TERMINOLOGY FOR CHEMICAL ANALYSIS OF STEEL PRODUCTS
3.1.1.1 cast or heat (formerly ladle) analysis —
applies to chemical analyses representative of a heat of steel
as reported to the purchaser and determined by analyzing a
test sample, preferably obtained during the pouring of the
steel, for the elements designated in a specification.
3.1.1.2 product, check or verification analysis —
a chemical analysis of the semifinished or finished product,
usually for the purpose of determining conformance to
the specification requirements. The range of the specified
composition applicable to product analysis is normally
greater than that applicable to heat analysis in order to take
into account deviations associated with analytical reproducibility
(Note 1) and the heterogeneity of the steel.