Why Banks give more discounts/offers on Credit Card as compared to Debit Cards?
Yes of course you are right about both of your points. The fee charging the credit card POS transaction is about 2% to 3% depending on the company. The fee charging to debit card transaction is about flat 25 cents or lower.
For online transaction, the credit card fee can be as high as 4%, and the debit card fee can be negligible. Banks make more money on credit card.
So, to answer your question:

Credit department usually have more money to make promotions.
Average people (in US) have almost zero savings so they cannot use their debit card very often. But everyone has a credit card.
Of course, credit card can default, and the bank can legally charge hefty interests.

And as mentioned by Brian, competition is an important reason.