Fiqh is the system and the Quran and Hadith or the sunnah of sayyidina muhammad (saw) are the source for deriving rulings for the Islamic way of life. Without fiqh one can get totally lost or seriously misguided. see here.
These schools known as Madhaabs play key roles in shari’ah rulings. In a literal sense one can say that shariah is of 4 types, but in reality there is only one shariah law which is understood and interpreted slightly differently in each school. Worth noting is the comment by Shaykh Nuh Keller in “The Reliance of the Traveller” – 75% of Rulings are identical in all four schools.
The remaining 25% are slightly different to each other but all have roots in the Quran & Hadith. One imam came to his conclusions with a certain text on a certain issue while another imam used different texts and arrived at a different conclusion henceforth.
Ahlus Sunnah accept all four schools as acceptable but chose to strictly follow one school, which salafi and wahabies refuse to accept. The debate with anti-madhabists can go on and on, so it is worthless debating whether one can or is allowed to adhere to only one madhaab or not.
Another practice related to this which salafies condemn is taqlid, which they call blind following but it is best interpreted as trusting a highly learned person or a highly religious authority. One could also explain it to be the acceptance of an opinion (the essence of madhabs), that of an expert in the field without asking for proofs. see here.
Hanafi Fiqh Maliki Fiqh Shafi’i Fiqh Hanbali Fiqh