The Madhahib are one of the great blessings of Islam and they are an actualization of where Allah (SWT) says
Indeed, it is We who sent down the Qur'an and indeed, We will be its guardian. (Al Hijr, 9)
The reason I say this is because it is incumbent upon the Muslim to be connected to the Prophet (SAWS) in his actions, words and belief. Therefore, the madhahib provide a chain of transmission from the student learning the books all the way up until the words or the actions of the prohpet that relate to the practice of a certain verse. The Prophet's words and actions are simply the practice of the Qur'an, just as our mother Aisha (RA) said when asked about the messenger that "His Character is the Qur'an".
Now, the great Tabieen who followed the Sahaba ensured that we not only have compiled and verified versions of his sayings (the Ahadith), but they also made sure to create a methodology of usul ul fiqh (principles of deriving rulings) from the Qur'an and the reported actions of the messenger. These tabi'een laid down principles as to how to derive a ruling. Generally, the Qur'an came first and then the reported sayings of the Messenger (SAWS) and then, for example in the Imam Malik's madhab, the amal (actions) of the people of Medina as that is where most of revealed law took place, and then the ijmaa (concensus of the early salaf), and then qiyas (analogy), and then the customs of the people in the location (Generally last).
Now there are differences between the madhahib and within the madhahib themselves. This is because of how they apply the evidences, both across the text and the text itself. An example of this is the Prophet (SAWS) ordering us and informing us about the reward of "Whoever fasts from (Min) the month of Sha'ban". Imam Shafi'i took that particle min to be indicative of from the month of sha'ban or within the month of Sha'ban, whereas Imam Malik took it to mean Min (starting from) the month of Sha'ban to the next Ramadan. Thats a difference from just one word.
Sometimes, in the same madhab, you can have differences based on the understanding of a hadith. For example, the dominant opinion in all the madhahib (including the Hanbalis) and in the Hanbali madhab is that abandoning the prayer out of laziness does not make one a Kaffir. The hadith where the messenger said "Baynana wa Bayanhum" (Between us and themmm (is the salah)) does not indicate that not praying means you are a kaffir; rather, it means that the person is like them. The indication of the dominant position of the madhahib is indicated by other hadith such as the messenger (SAWS), in the hadith of Tirmidhi, informing us that the eprson who does not pray, Allah may punish him or forgive him, or the messenger saying that whoever uttered La ilaha ilallah sincerely will not remain in the fire eternally.
Or another khilaf being the Malikis considering sperm najis (impure) because of the statement of Allah in the Qur'an that "Then He made his seed from a draught of despised fluid" (32:8). Whereas, the other madhahib consider it clean based upon the hadith of our mother Aisha (RA) about how she would scrape off dried semen from the clothes of the prophet without water.
So, these type of ikhtilaf are generally minor and they occur both within a madhab and involve the application of the principles of usul ul fiqh.
However, they illustrate the great blessing of Islam because the preservation comes within an established structure. If you come with a ruling regarding the deen, you have to come with the evidences that support that or else it will be rejected as being munkar or shaad. There are entire books written to compile such strange opinions and who brought them about.
It is also why the fitnah of the Salafis is so great. Because, they say they follow the Qur'an and the Sunnah when they are not qualified to do ijtihad of the primary texts and when they are largely following a small group of Scholars who hold minority views from the Hanbali Madhab. The way of knowledge in Islam, after the Qur'an, is to begin with the primary texts of a particular Madhab so as to perfect your worship and then gradually to learn the khilaf and then to learn the principles of deriving rulings so that you can see how those khilaf came to be. Even then, you would not be qualified to simply go into Sahih al Bukhari and say things willy nilly that contradict the pre-existing opinions of the scholars.
I would advise those who see knowledge to take a particular madhab and learn it from someone who is not Salafi. Because salafi brothers will claim the Shafi'i madhab, for example, and then give the rulings of Bin Baz or Uthaymeen (Raheemahumullahu Ta'Ala) that are in stark contradiction with the rulings and the principles used in the Shafi'i madhab. From there, read the books on usul ul fiqh (such as Sharh Ul Waraqat) and then gradually go through the ladder with the texts. Because for each Madhab, you may have 4 or 5 beginner texts, and their commentaries, 3 or 4 middle texts and their commentaries, and 1 or two advanced texts and their comentaries. Asides from that, you'll have compilations of the names of people who transmitted the madhab, compilations of the ikhtilaf, and ect. Often times, you'll find someone like Imam Shafi'i in a maliki text or vice versa because the madhahib were not founded on sectarianism but rather for the preservation, transmission and practice of authentic knowledge of the words of Allah and the actions of his messenger (SAWS) and the actions of those blessed individuals who followed them.
