What is a custodial vs. non-custodial wallet?

When it comes to custodial and non-custodial wallets, it is what the name sounds like.
Non-custodial wallets are wallets that are independently held by the user. No one else can control your assets or the way that you choose to interact with them. There’s also no third party that is charging transaction fees when you do something with your assets. The downside is that in order to buy crypto using your credit card and directly fund your non-custodial wallet, you’ll often pay higher fees than you would when compared to funding a custodial wallet.
As mentioned in the last section about wallets, losing the non-custodial wallet’s private key or seed phrase can mean that you lose access to your wallet and there is no way to recover it. While you have full control, you also accept the full risk in case something goes wrong. The responsibility is squarely on you to manage the access to your funds.
On the other hand, a custodial wallet is a wallet that you keep with a crypto trading platform, such as Binance or Coinbase. When you sign up for an account, you don’t get keys to your own wallet. Instead that third party controls your private keys. The upside is that you can always reset your password to get access back to your account and therefore your wallet. The negative is that you have to be able to trust the third party that controls your wallet, and you have to put up with the transaction fees charged by that platform.
While custodial wallets are theoretically safe to use, there are a lot of risks that are out of your control with these wallets. If the exchange is hacked, there’s a chance that you could lose assets as happened as a result of a BitMart hack in 2021. Another problem is that the exchange could stop providing service to you and freeze your account. Certain exchanges are worse than others in this respect. There is also the added inconvenience that using a custodial wallet comes with certain restrictions, such as not being able to hold DeFi assets or not being able to move your coins to another wallet without a waiting period of multiple days, during which market shifts could cause you to lose money or miss opportunities to trade at advantageous rates.