What is the difference between sects and schools of thought? How were they formed? And are all of them correct or not?

Allah Almighty legislated one religion for all messengers and forbade division. The religion is one, with no disagreement within it, and whoever disagrees with it are misguided factions. As for the legal schools of thought (madhahib fiqhiyyah), they are based on independent reasoning (ijtihad) in subsidiary matters to meet the needs of Muslims in knowing the rulings of their religion, and they do not differ regarding the fundamental principles of Sharia. These schools of thought emerged as jurisprudential schools to find lawful solutions for new and evolving situations. The differences among the scholars who founded these schools are due to their independent reasoning; for the mujtahid (one who exercises ijtihad), if he is correct, he receives two rewards, and if he errs, he receives one reward. The authentic schools of thought are attributed to imams known for their piety and adherence to the Sunnah, the most famous of which are the four madhahib.