I will appreciate further explaination about this, which wallets are non-node wallets?
Essentially, anything that isn't Bitcoin Core isn't a full node. There are a couple of other alternative full node software packages, such as Bitcore, bcoin, and btcd, but I wouldn't worry about them. All the wallets which you might be familiar with, things like Electrum, Mycelium, Coinomi, etc., are not full nodes.
Are non-node wallets the custodial wallets?
All custodial wallets are non-full nodes, but not all non-full nodes are custodial.
A custodial wallet is a wallet where someone else holds your coins.
A non-custodial wallet is when you hold your coins yourself. You can either hold them in a full node wallet such as Bitcoin Core, or a non-full node wallet such as Electrum.
Also, if I have an open source wallet like bitcoin core and eletrum, are they example of bitcoin client?
Bitcoin Core is a bitcoin client. Electrum is not - it is just a wallet.