Another sub-category or classification would be open-source vs. closed-source wallets. It's undebatable that non-custodial (NC) wallets are better than custodial but let's keep in mind that a lot of NC are closed-sourced. The basic difference between the two is that there are more eyes to check the codes for open-source unlike the other one where only a select few (usually the dev team only).
If you are looking for a list of open-source hardware wallets, here's one https://www.altcoinstalks.com/index.php?topic=314728.0
It's good point. Although few wallet such as Trust Wallet could be classified as partial open-source since they only release code for their "core" library which can be seen on https://github.com/trustwallet/wallet-core. Although few people disagree since there's no way to verify that.
Although it's better than a completely closed-source, I don't really see the excuse of not keeping everything open. Competition? Valid but still doesn't override the public
trust and respect they could get. To make things simple, I just consider anything that's not fully open as closed.