If all the madhabs are said to follow Allah's Messenger (ﷺ), then why are there so many differences?
Wouldn’t their sources be the same (Qur'an, Sunnah, etc.) and hence have the same rulings?
Or is it that their understandings that differ?
This is a very good question and although it requires a very long explanation, I will try to summarize my answer.
Let us assume that there are three students (Blue, Green and White) who attend your classes on a daily basis. One day, Blue migrates to Canada, and after 5 years, Green migrates to Syria. After 15 years, you pass away. Blue might not have the knowledge of what transpired before your demise from the time he left until you passed away. The same can be said about Green.
Now imagine the Sahabah and how they spread all over the world. This meant that some went and never got to know about other ahadith of the Prophet (ﷺ) and this is among the many reasons of difference in the madhabs.
The difference might also come from the fact that there are certain words that contain multiple meanings. Each and every ‘alim might understand them differently and this will lead to a difference of opinion. 
 Dr B Philips, The Evolution of Fiqh 121 - 131< Back to Questions