This is honestly a pretty good summary of the similarities between chaumian ecash tokens and gift cards.

My perspective on this is that ecash tokens have some crucial differences with gift cards:

1. eCash as implemented by cashu or fedi is several orders of magnitude more private than gift cards, because nobody is going face-to-face with a merchant to spend the card or being caught from surveillance cameras. For online usage, most of the times an account is required to redeem gift cards, so the privacy problem still exists (also because the majority of merchants don't let you refill an account with gift cards if you don't put in an identifiable payment method like a credit card or bank account [at least this happens where I live]).
2. A mint can either permit blindly agree to all the requests to the server (eCash minting or burning) or agree to none. There is no such thing as as blacklisting of some users. On the flip side, gift card providers can deny YOU the usage of the gift card but allow all the others to use it...this is because of the account-based model for gift card redemption (in an online environment) and for the face-to-face aspect for in-person usage.
3. In Cashu there is no such thing as user, only coins exist. Moreover, coins are minted in such a way that amount correlation is not possible. In other words, if I request 13 sats (in eCash) to a cashu mint, the mint will blindly sign 3 different coins, one coin of 8 sats, one of 4 sats, one of 1 sat. This means that coins are potentially separately spendable. Gift cards simply work as a single-tranche transaction for any amount. For uncommon gift card sizes, some kind of amount correlation can be done (at least theoretically).
4. Gift cards do not have a common settlement layer between gift card providers, whereas eCash tokens potentially have common settlement layers, at least in the cashu and fedi implementations (LN as a settlement layer).

Your examples are really interesting and I consider your perspective really interesting. Consider my 4 points as and add to what you said.