Difference between "validation" and "verification"

I think the subtle difference would be in that "verification is validation by empirical means".

empirical: Based on, concerned with, or verifiable by observation or experience rather than theory or pure logic.

Taking your example, checking the format of an email address is done by logic, to see if you have <something>@<something>.<xxx> format. But, you cannot logically tell by looking at the string that it is a genuine email address.

Validate comes from the Latin validus, meaning strong.

Verify comes from veritus, meaning true.

We often say that an argument founded on strong principles is valid. For instance:

"I cannot see the stars. I have no way of knowing if they're still there. For all I know, they might have disappeared, and scientists around the world are lying when they say they're there."

"Your argument is valid, but I'm pretty sure scientists have better things to do."

On the other hand, we could say,

Scientists today verified that the stars did in fact disappear during daylight, when astronauts aboard the shuttle "Scepticism" travelled above the atmosphere for the first time and found that no stars above the daylight side were visible.

The biggest difference is in the hypothesis. A valid hypothesis is one which appears to have supporting evidence, or which has not been disproven*. A verified hypothesis is one which has been proven (in this case, the anti-hypothesis).

Let's say that your hypothesis is that the user has entered their email address correctly. The address is valid if it's well-formed, or if you can send an email to it - it exists - but only verified as the user's address once the link sent in the email is clicked.

Or perhaps your hypothesis is that entries in a form are correct. It might be valid if all mandatory fields are filled, but only verified once the business rules associated with the different fields have been checked too.

Because verification necessarily involves validation, there may be some flexibility about what you define as valid. The purpose of validation is usually to provide quick feedback about what might be wrong, whereas the purpose of verification is to make sure it's right.

(*Can anyone verify that "disproven" is a word? Please validate my assumption.)

In your examples, you use both words correctly. I wouldn't use them interchangeably.

Generally, when you validate something, you make it officially acceptable or approved, especially after examining it, e.g. External validation of a teacher's assessment is recommended.

When you verify something, you show that it is true or accurate, e.g. State officials provided verification of the documents.

I saw an ad for this question on the Computational Science Q&A site, so if you'll allow me to provide an answer from that perspective...

Where I come from, to "verify" means to make sure you are solving the equations correctly. Does the code you implemented accurately compute the equations you mean to solve?

To "validate" is to make sure you are solving the correct equations. Is the model you implemented an accurate representation of the physics you are attempting to emulate? Does it compare well to observed behavior?

There is a lot of work in the computational science community on "V&V" and every document on them starts with this type of definition.