Salam, 

Thank you for your question. The word “khalifa” in Arabic literally means “successor“.

In the verses to which you are referring, the word “khala’if”, is the plural form of khalifa. God is saying in these verses:

{And they denied him (Noah), so We saved him and those with him in the ship and made them successors, and We drowned those who denied Our signs. Then see how was the end of those who were warned. Then We sent after him messengers to their peoples, and they came to them with clear proofs. But they were not to believe in that which they had denied before. Thus We seal over the hearts of the transgressors.}

God sent Noah to his people with His message to worship Him Alone, but all of them rejected Noah, except for a few from his family. God then describes how prophets after Noah suffered from the same problem. Those who will not believe have their hearts sealed up and no one can lead them to belief. With respect to the people of Ad, they were sent prophet Hud, peace be upon him, but most of them, similar to the people of Noah, would not believe:

{And O my people, ask forgiveness of your Lord and then repent to Him. He will send [rain from] the sky upon you in showers and increase you in strength [added] to your strength. And do not turn away, as criminals.}

The people of Ad were the successors of the people of Noah in that they were of Noah’s lineage. But human nature being what it is, they grew powerful and arrogant and saw themselves in no need of God. Hud was sent to them as a prophet to return them to the worship of God but they refused, and were brought to ruin by God’s Will.

The “one khalifa” to whom I believe you are referring, would be the successor of prophet Muhammad, peace be upon him, who is known to be Abu Bakr as Siddiq, may God be pleased with him. He was chosen to be the leader of the Muslim community after the death of prophet Muhammad. After the death of Abu Bakr, Umar ibn ul Khattab was elected leader, but to avoid using a cumbersome title like, “Successor of the Successor of the Prophet of God”, his companions named him “Ameer ul Mu’mineen” or “Commander of the Faithful”. Subsequent “khalifas” were given this title by their followers as well. So as you can see, there is really no contradiction in the Qur’an regarding the concept of khalifa, and the traditions of Muhammad’s companions, may God be pleased with all of them.

Hope this helps. Salam.