What is the authenticity of the saying, "There are no parties in religion," attributed to the Prophet, peace and blessings be upon him, and what is meant by the four schools of thought (Hanbali, Shafi'i, Maliki, Hanafi), and what is the difference between them?

No Hadith with this exact wording has been found. However, the Lawgiver (Allah) condemned those who split up their religion and became sects, as Allah Almighty says: "Indeed, those who divided their religion and became sects - you are not [associated] with them in anything." (Quran 6:159) This blameworthy division is to abandon the religion entirely or partially. As for the four Madhhabs (schools of thought), their differences are in subsidiary matters, and the Imams used to encourage adherence to the Sunnah if it contradicted their own opinions.