Difference between assay and purity?

Answer 1

Assay is the quantitative determination of the amount of a component in a sample.
Purity is the determination of the impurities in the sample. It can be quantitative, semi-quantitative or qualitative.
For example : if you dissolve 4 grams of compound A (with no impurities in it) in 6 grams of water, you get a solution of compound A with 100% purity and 40% assay.
From the ICH Guideline Q2A (Validation of Analytical methods) :
"- Testing for impurities can be either a quantitative test or a limit test for the impurity in a sample. Either test is intended to accurately reflect the purity characteristics of the sample. [...]
- Assay procedures are intended to measure the analyte present in a given sample. In the context of this document, the assay represents a quantitative measurement of the major component(s) in the drug substance."