In most cases, people apply for a new card because the old one has expired. In this particular context, the card number does not change. You can report your card lost or stolen if you lose it or think someone stole your credit card information. If you report your card lost or stolen, Capital One will immediately block the lost card so that no one else can use it and issue a replacement card with a new card number.
Usually, the card number doesn't change when you get a new debit card. However, the expiration date and CVV (card verification value) will be different on the new debit card. This will not affect your credit rating. A replacement card should be considered part of the same credit card account when it comes to your credit reports.
The real answer is that it depends because it's up to the credit card issuer to follow the right path when issuing a replacement credit card.