What is the difference between linking my CDP account to a savings account vs trading account?

CDP have to be linked to both.

Trading account to transfer your shares when you purchase/sell SGX stocks.

Savings/Current account to pay you dividend or your "cash-out" when you sell shares.

If you intend to invest in Singapore stocks, you will need a CDP account. A CDP account is needed to store your shares. If a brokerage lets you invest and does not require you to open a CDP account, it probably means that the brokerage is holding your shares for you (ie: they are the custodian of your shares). Not that is bad, but some people do not like someone else holding their shares for them.