Both are called proofs and they answer different questions. Confusing them is how orders get approved on the strength of something that was never going to catch the problem.
A virtual proof
A digital mock-up: your artwork placed on an image of the product, with dimensions and position marked. It confirms that the right logo is the right size in the right place, in the right colors.
It is fast, it costs nothing, and it is what most orders are approved on. What it cannot show you is how the decoration will actually behave on that material.
A production proof
An actual decorated unit, produced on the real product by the real process. It confirms the physical result: how the color sits on that substrate, how a fine detail holds at that size, how an imprint wraps a curve.
It costs time and sometimes money. It is the only thing that answers the question that matters on a large or unfamiliar run.
Which to insist on
Virtual is sufficient for reorders of known products, small runs of familiar stock, and simple one-color decoration. Production proofs earn their cost on large volumes, custom manufacturing, difficult substrates and multi-product programs that have to match each other.
Approval means what it says
Whatever the type, approval is the point at which the artwork becomes the standard. Nothing should enter production before it, and what is approved is what the run is inspected against — which is why a rushed approval is rarely a saving.
Keep the approved file
It is the reference for reorders and the reference if something is disputed. It should be retrievable a year later, not sitting in one person's inbox.
Pre-production samples cover the physical version in more detail, and bulk merchandise covers how the approved proof is used across a run.