I repeat this almost every time this topic comes up:

With a credit card, you can say that the charge was fraudulent and they will take the charge(s) off and you're not on the hook. With a debit card, you're out the money of the fraudulent charge while the bank investigates. From my personal experience, this can take a few days to 3 weeks before the bank puts the money back in your account. If the charge happens to put your account into overdraft, you may still have to pay the overdraft fee which may be hard to get overturned.

I pretty much only use my debit card as an ATM card. Very rarely do I actually use it as a debit card (there are rare instances where I may need to)

Conclusion: Don't use your debit card online if you have a credit card.

With the bank account, they may not reverse fees or other issues that arise as a result. For example, I had a fraudulent charge on a debit card. They reversed it, which is fine, but i was still hit with an overdraft because of a scheduled ACH payment which, at that time, dragged me into negative balance. So there are differences between debit and credit cards.