What is the difference between verification and validation?

General definitions

On one hand, I've been working in embedded systems, specially in aeronautics (were DO178 applies to software) and i'm used to these definitions:

• validation: check with test, inspection, analysis, demonstration, that the final product/service, fulfill the customer requirements. "Are we building the product right?"
• verification: check that each process is done correctly. e.g.: all the customer requirements are covered by a test, inspection, analysis or demonstration. Your product could be faulty, but your documentation is correct. "Are we building the right product?"

Is my interpretation correct?

On the other hand, I've seen in the application world (like in ISTQB certification) that:

• validation has the still the same meaning (but restrictive to a complete product)
• verification is also used to describe a validation process, but not for a full product/system: for sub-systems. Is my understanding correct? Is it a common practice?

In the context

In our company we are making appliances, and in our team/department, we are making sub-system for those appliance (GUI). Some colleagues of mine are using the "verification test" term to describe the activity of functional test on our sub-system, considering we are testing a part of the appliance. They say the validation tests cannot be done as our sub-system is not the final product.

In other words, they are saying that, because the customer ask for an appliance, they are not considering themselves and the other members of the department as customers for the sub-system. Therefore, the activity of functional testing is not a activity of validation, because does not correspond to the definition "Checking that the product does what the clients asked for".

Here comes my question: Is there any "TRUE" standard definition of verification and validation? How can I make myself understood if everybody use a same word to describe 2 distinct activities?

Note: a first question was asked here but was not referring to any documentation and thus subject to opinion-based answers