Asalaykum Wa Rahmatullah,
The schools which you have listed are Islamic schools of thought but not all of them are necessarily Sunni.
The three main Sunni schools are:
The Ash'ari school is named after the eponymous founder, Abul Hassan Al-Ash'ari. He passed away 324H. His main objective was to find a rational middle-path between the way of the Mu'tazilites (non-Sunni sect) and the textual literalists. Many great Sunni scholars agreed with his theological ideas and followed him in his methodology including Al-Nawawi, Al-Ghazali, Al-Bayhaqi, Al-Juwayni, Al-Suyuti, Ibn-Asakir and many others. A large majority of the followers of the Shafi' and Maaliki jurisprudential schools of law embedded Ash'ari theology into their schools.
The Maturidi school is named after the eponymous founder, Abu Mansur Al-Maturidi. He passed away 333H. He had similar objectives to his contemporary Al Ash'ari as well as wanting to combine and codify the views of the Hanafi scholars as per the teaching of Imam Abu Hanifa and his disciples. The majority of the Hanafi scholars during and after his time adhered to his theological leanings.
The Ash'aris and Maturidis do not have many differences and Shaykh Saeed Foudah has a small booklet written in Arabic detailing the few differences. They welcome the use of rationality and seek to find a middle ground between using rational syllogisms for scripture that seems irrational on its surface. For example, there is a Hadith which states that God descends during the last third of every night. Pure rationalists will argue that this defies the attribute of God not being contained by space. Hence, they will reject this narration. However, the Asha'ris and Maturidis will attempt to reconcile this narration and not reject it outright. They will use external evidences as well as linguistic proofs in order to demonstrate that this means God's mercy (and in another opinion, the Angels) descend during the last third of the night. This way, they do not reject scripture and they do not compromise on breaking rational principles for God.
The Athari does not have an eponymous founder like the other two. Rather, the term Athari goes back to the triliteral root: Hamza, Thaa and Raa. The linguists define this as meaning a residue. Eventually, this came to be used for Islamic scripture. This would include sayings of the Prophet Muhammad PBUH, the sayings of his companions and sayings of the followers of the companions. The name is used to denominate a strong adherence to the text and to avoid extreme uses of analogies and metaphors. The champion of the school was the famous Imam Ahmad Bin Hanbal (died 241H) who was also the founder of the Hanbali school of law. This is why majority of the adherents to the Hanbali school of law would end up following this theological branch. Their theological approach was to not delve into the attributes of God but rather to defer the modality of the attributes of God to Him.