You're getting all worked up over semantics. Standard checking and savings accounts are both demand accounts because no advance notice is required to withdraw funds. It's that simple.

I still don't understand the difference between the two deposits. Wikipedia (and my book) say that:

Demand deposits are funds held in demand deposit accounts in commercial banks.

Savings deposits are accounts maintained by retail financial institutions that pay interest but cannot be used directly as money in the narrow sense of a medium of exchange.

I understand that check is a form of demand deposits (in a sense that it is "on demand" or can be demanded at any time without prior notice), but how about savings account? Are they demand deposits or Savings deposit?

I'm confused since by the definition we can say that savings account is part of saving deposits (because they pay interest) but they also can be said as part of demand deposits (because we can "demand" them at any time, lets say by using ATM).

Thanks for your help!!