What are the main differences between the beginning of the Umayyad state's rule and the era of the Rightly Guided Caliphate, which led it to be described as a kingdom rather than a caliphate following the prophetic methodology?

The main difference between the Rightly Guided Caliphate and the kingship of Mu'awiyah lies in the method of appointing the ruler. The Rightly Guided Caliphate was founded on selection and consensus, whereas Mu'awiyah's rule was established through conquest and inheritance. Nevertheless, the meanings and objectives of the Caliphate persisted during Mu'awiyah's time, even though the Caliphate of the Rightly Guided Caliphs was more complete. Ibn Taymiyyah stated that Mu'awiyah's rule was a kingship and a mercy, and that what came after it was an oppressive kingship, thereby explaining the Hadith of the Prophet, peace and blessings be upon him. Similarly, the caliphates of Abu Bakr and Umar were more complete than those who came after them.