(If anyone wants to see the full original context, this seems to be it.)
I think OP is simply being misled by "requirements" appearing in both definitions, together with the fact that specified is in the first, and specific in the second. Reading the full text, it's obvious...
Verification = ensuring the software addresses everything in the specified requirements.
Validation = ensuring the software addresses the specified intended use.
An example of the difference arose a few years ago in a company I had dealings with. The customer (a nationwide group encompassing many bus companies) wanted to store all their bus ticket data within a single centrally-maintained industry-standard RDBMS database. But the requirements specification said nothing about speed of processing.
After a development team had spent over a year producing a system which seemed to meet the specification, it became apparent that on any hardware the customer could realistically hope to afford, loading each new day's data would probably take more than 24 hours.
One could of course say this debacle was caused by a deficient specification - but such mistakes are bound to happen sometimes. And that's what OP's "validation" process is supposed to catch.
EDIT: It seems OP isn't satisfied with my way of describing the difference, so I'll quote from the start of the chapter I linked to above...
[verification is] “Confirmation that work products properly reflect the requirements specified for them”. In other words, verification ensures that “you built it right”.
[validation is] “Confirmation that the product, as provided (or as it will be provided) will fulfill its intended use”. Therefore, validation ensures that 'you built the right product'.