Are certain English words cognates to Old English words?
They are both cognates, and borrowings.
They are indeed related to the Old English words, which makes them cognates. However, because they (as I take it) fell out of usage before being borrowed into the language, they are also what the people who spoke at the time took them to be: borrowings. They were not aware that cognates once existed in a past form of their language. That is why it is both.