App Store & iTunes gift card vs. apple store gift card

No. App Store and iTunes gift cards only work in those online stores.

The only option is for you to sell the card.

No, the App Store & iTunes gift cards can only be used, of course, for App Store and iTunes purchases, and Apple Music and iCloud Storage subscriptions. For purchases made in the Apple Store, for physical products you would need an Apple Store gift card.

If you own an iTunes gift card, you cannot get an Apple Store gift card in exchange. So, the answer is no :(

This might help: Gifting - Shopping Help - Apple

No