Sorry to check in late on this topic - I have just rejoined the land of internet.
IMO, "hand-made" belongs to the same class of throw-away words as "perfect balance" and "best gun." These words appear to have meaning but actually lack a general definition; unless the definition is stated, there is a good probability of confusion of communication. "Hand-made," as stated above, can mean how the gun was fabricated, imply a high standard of craftsmanship, and/or imply the gun is an art object rather than just a tool.
For example, "perfect balance" can mean the teeter-totter point of the gun or an attempt at subjective summation of the gun's handling. I always state that my work refers to the teeter-totter point. Thus, "balance" is a fact of the gun and "perfect balance" has meaning only in the context of the specific gun and a specific shooter. This is just like "perfect stock dimensions" having meaning only in context of a gun and a shooter.
So, we might say, "This gun was hand-made in a small shop by master gunmakers using hand tools and manually controlled machine tools." Or, "This gun was hand-made to "best work gun" standards (where "best work" refers to the gun trade standard of workmanship, material, and design for a period of time ("London best gun" refering to a "best work gun" in the London style)). And, we might say, "This is a "hand-made" gun of art quality fit and finish.
User of "hand-made" without definition by a seller generally implies that the seller hopes the buyer will then see the guns as a very special speciman.
AT least that is how I see the word.