First, it is better to stay away from these articles as sources of learning, most of which are full of misleading information that has become circulated as facts.
I mean Cointelegraph, binance academy, crypto.com
And let's not forget that some of these articles are biased, as were some articles on Bitcoin.com
a wallet is that software that manages your private keys, if you do not have access to the private key, then you are not using a wallet.
Therefore, the word custodial wallets and non-custodial wallets has no meaning, because if you do not have the private key, then they are not not using a wallet. I can understand it in the formulation of whether you are the only one who can access that private key, or is a third party able to access it.
To make it simple:
If you do not have a private key, this service is not a wallet.
You can manage the wallet from a browser. It is a web wallet.
Otherwise, the divisions are not technical, but rather come from these poorly worded articles.
https://github.com/bitcoin/bips/blob/master/bip-0032.mediawikiWell as you wish sir, you are right. We will not disagree.
This is a disagreement over terminology only, and nothing more. Do all people, in your opinion, have the same academic knowledge as you? of course not.
It is certain that the one who stores his coins on the Internet (or what some call a web wallet) is a beginner, because if he had enough knowledge, he would simply know that (it is not your key, not your coins) and he would not have stored his coins there, so how can you convince such This person that this service on the website (is not a wallet).
I'm just using common terms that all people (beginners and experts) understand and haven't created anything new.