As a general rule, the "The Gibson" headstock inlay indicates a more expensive instrument with higher grade appointments than one with just "Gibson". For one thing, the "The Gibson" logo is always inlaid, while the plain "Gibson" logo is usually a decal. That doesn't necessarilly mean they sound any better, just that they're fancier.

Some other makers have adopted the inclusion of the "The" to indicate their own premium grade instruments. For example, Weber Mandolins' top of the line F-5 Fern carries a "The Weber" logo.