Custodial services work by analogy with depositories: they store customer funds and private information on the server side. In the case of cryptocurrencies, in addition to personal data, custodial wallets store private keys, passwords and seed phrases (mnemonic password). In other words, the client's data may be compromised by third parties if they gain access to the company's servers.
Custodial services pose a threat to the anonymity and security of users. In addition, custodians can fully control user accounts and cryptocurrency storage: block funds, set limits on input/output, and much more. And the withdrawal request can be processed by the company on an individual basis.
There is a partially custodial cryptocurrency wallet. For example, there are limits on the amounts for exchange and withdrawal, but private keys and passwords are not stored.
Cons: assets are not under user control, KYC/AML user verification is required, there is a threat of asset loss if the platform is compromised.
Non-custodial wallets are completely autonomous. This means that no one except the users themselves can manage the wallet balance. In fact, the wallet itself acts as a bank and is controlled by a program code, which prevents interference on its part. To access such wallets, a private key and a seed phrase are required, which the user must securely store. In addition, you need to make several copies.
Storing cryptocurrencies in a non-custodial wallet is entirely the responsibility of the users themselves. If you lose all the private keys, passwords and the seed phrase of the wallet, then the funds will be irretrievably lost.
Advantages of non-custodial wallets:
1) Full access to funds. Only the users themselves decide what to do with the account.
2) Secure storage of cryptocurrencies. Hacking a personal wallet, especially if it is autonomous or hardware, is almost impossible.
3) No transaction delays.