Short answer
Ash'ari aqeedah is a Sunni school of creed built on the method of Imam Abu al-Hasan al-Ash'ari (d. 324 AH). With the Maturidi school, which most Hanafis follow, it has been the creed of most Sunni scholars through history. Atharis, also counted among Sunnis by many, avoid rational theology and keep to the wording of the texts.
Deobandi and traditional Hanafi institutions follow the Maturidi school and regard Ash'aris as fully within Ahl al-Sunnah wal-Jama'ah; the differences between the two are few and mostly in wording. Declaring other Sunnis disbelievers over these questions is wrong.
The four schools agree on this.
Explanation
Abu al-Hasan al-Ash'ari was a leading Mu'tazili theologian in Basra who left them and spent the rest of his life defending the creed of the early Muslims with their own tools of argument. His followers, such as al-Baqillani, al-Juwayni, al-Ghazali and al-Razi, made the Ash'ari school the main creed of the Shafi'is and Malikis.
At the same time, Abu Mansur al-Maturidi in Samarqand (d. 333 AH) systematised the creed of Abu Hanifa. His school spread with the Hanafis, through texts like al-Aqa'id al-Nasafiyya. Deoband's statement of creed, al-Muhannad 'ala al-Mufannad, says its scholars follow al-Ash'ari and al-Maturidi in belief. See What is aqeedah?
Ash'ari and Maturidi differences are a short list, often counted at around a dozen. Examples: Maturidis hold that reason alone obliges a person to know Allah, while Ash'aris tie obligation to revelation; Maturidis count takwin (Allah's bringing into being) as a distinct eternal attribute; and they word differently whether Allah's acts are tied to wisdom. Scholars of both treat these as differences within the house.
The Athari approach affirms the attributes in the texts, such as Allah's hand or His rising over the Throne, and declines to discuss their meaning in theological terms. Ash'aris and Maturidis agree Allah is not a body and either leave the meaning to Allah (tafwid) or explain it in a way fitting His majesty (ta'wil). All three affirm that "there is nothing like unto Him" (42:11) and that the unclear verses are read in the light of the clear ones (3:7). See Where is Allah? and both of Allah's hands are right hands.
The evidence
Quran, Surah Ash-Shura 42:11
فَاطِرُ ٱلسَّمَٰوَٰتِ وَٱلْأَرْضِ ۚ جَعَلَ لَكُم مِّنْ أَنفُسِكُمْ أَزْوَٰجًۭا وَمِنَ ٱلْأَنْعَٰمِ أَزْوَٰجًۭا ۖ يَذْرَؤُكُمْ فِيهِ ۚ لَيْسَ كَمِثْلِهِۦ شَىْءٌۭ ۖ وَهُوَ ٱلسَّمِيعُ ٱلْبَصِيرُ ﴿١١﴾
[He is] Creator of the heavens and the earth. He has made for you from yourselves, mates, and among the cattle, mates; He multiplies you thereby. There is nothing like unto Him, and He is the Hearing, the Seeing.
All Sunni schools of creed build on this verse in the attributes.
Quran, Surah Aal-i-Imraan 3:7
هُوَ ٱلَّذِىٓ أَنزَلَ عَلَيْكَ ٱلْكِتَٰبَ مِنْهُ ءَايَٰتٌۭ مُّحْكَمَٰتٌ هُنَّ أُمُّ ٱلْكِتَٰبِ وَأُخَرُ مُتَشَٰبِهَٰتٌۭ ۖ فَأَمَّا ٱلَّذِينَ فِى قُلُوبِهِمْ زَيْغٌۭ فَيَتَّبِعُونَ مَا تَشَٰبَهَ مِنْهُ ٱبْتِغَآءَ ٱلْفِتْنَةِ وَٱبْتِغَآءَ تَأْوِيلِهِۦ ۗ وَمَا يَعْلَمُ تَأْوِيلَهُۥٓ إِلَّا ٱللَّهُ ۗ وَٱلرَّٰسِخُونَ فِى ٱلْعِلْمِ يَقُولُونَ ءَامَنَّا بِهِۦ كُلٌّۭ مِّنْ عِندِ رَبِّنَا ۗ وَمَا يَذَّكَّرُ إِلَّآ أُو۟لُوا۟ ٱلْأَلْبَٰبِ ﴿٧﴾
It is He who has sent down to you, [O Muhammad], the Book; in it are verses [that are] precise - they are the foundation of the Book - and others unspecific. As for those in whose hearts is deviation [from truth], they will follow that of it which is unspecific, seeking discord and seeking an interpretation [suitable to them]. And no one knows its [true] interpretation except Allah. But those firm in knowledge say, "We believe in it. All [of it] is from our Lord." And no one will be reminded except those of understanding.
Unclear verses are understood through the clear ones.
Where the ruling is recorded
- al-Muhannad 'ala al-Mufannad (Khalil Ahmad Saharanpuri), Opening answers on creed. States that the Deobandi scholars follow al-Ash'ari and al-Maturidi in belief.
- al-Rawda al-Bahiyya fima bayna al-Asha'ira wa al-Maturidiyya (Abu Udhba), The list of differences. Lists the points on which the two Sunni schools differ.
- Sharh al-Aqa'id al-Nasafiyya (al-Taftazani), Introduction. A standard Maturidi text that notes where the Ash'aris differ.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.