Attribute Sampling
In attribute sampling, data is in the “attribute” form, and the result either conforms or does not conform.
Attribute data is the simplest kind. You sample some number of items and you classify each item as either having some attribute, like being defective, or not. You will have some standard for what a defective item is -- like broken, scratched, non-functional, etc.
Variable Sampling
In variable sampling, data is in the “variable” form, and the result is rated on a continuous scale that measures the degree of conformity.
Variable sampling is about checking “how much”, “how good”, or “how bad”.
Variables data contains more information than attribute data per data-point. This is because it allows you to assess "how much" or "how bad" or "how good" rather than just "yes its defective" or "no its not defective".
Examples
Is the color black or not, is attribute data. What shade of gray it is, is variable data.