Credit score vs. credit history--an issue for our kids?

I tend to think it has more to do with the issuing company. My Chase Visa was cancelled last week due to several fraudulent charges. They told me 7 days for the replacement card and the credit limit happens to be very high. I thought about requesting overnight delivery but didn’t think it was that important. This isn’t the card I use primarily so there’s no real problem waiting. If it happens to the card my husband and I use daily, I would definitely insist on overnight delivery.