The founding imāms put a condition on the use of their own words. It is not lawful for anyone to give fatwā by their statement until he knows where they got it from. That means knowing what it was drawn out of: the Qurʾān, the Sunna, the agreement of the umma, or qiyās.
Ṣāḥib al-Baḥr, that is Ibn Nujaym (d. 970H), argued that this condition was binding only on the scholars of that time. In our time, he says, it is enough to have learnt the view that came down to us. So giving fatwā by the Imām's view is allowed, and in fact required, even where we do not know his proof. On that reasoning, the later mashāyikh only gave fatwā against the Imām because the condition was not met in their own case.
Ibn ʿĀbidīn (d. 1252H) does not accept that conclusion. He gives a whole section of the sharḥ to answering it.
The dividing line is ability. A man who is able to weigh evidence may leave the Imām's view where his own study forces him to. A man who is not able to weigh evidence has to give fatwā by the Imām's view.
These are not the same kind of thing. A qawl is a position the mujtahid stated himself. So when two qawls differ, the difference goes back to him. A riwāya is what somebody else reported from him. So when two riwāyāt differ, the difference goes back to the men doing the reporting, not to him at all.
There is a habit in how the books word this. The view they prefer gets called his qawl, and is introduced with something like "according to him." The view they set aside stays a mere riwāya, and is introduced with "it is narrated from him." That is a real difference in wording. In practice, though, scholars often use the two words loosely for each other, so do not lean on the wording alone.
There is a further reason scholars end up disagreeing: the mujtahid himself was genuinely unsure. Either the evidence pulled both ways and left him with no clear preference, or one proof-text could be read in more than one way. Sometimes one of the two readings is later preferred, and gets called his qawl. Sometimes neither wins, and both stand as views of equal weight. On the numbering: the four causes listed below are the ones the source enumerates, each introduced with «ومنها». It brings this hesitation in separately, with «وقد يقال ... أيضا», so it is an extra observation and not a fifth member of that list.
First, somebody mishears. The Imām is asked about a case and answers with a no, saying it is not permitted. The listener mishears him, and then passes on what he thought he heard.
Second, he had an older view and later took it back. Some of the men around him learnt about the change and passed on the new view. Others never heard about it, and passed on the old one.
Third, he gave one answer working from qiyās and another working from istiḥsān. Each listener heard one of the two, and passed on the one he heard.
Fourth, he answered one question from two different angles: one answer giving the ruling itself, and one answer giving the safer, more cautious course. Again, each listener passed on the one he heard.
Ibn ʿĀbidīn then gives his own verdict on this list, in his own voice, his "qultu". He says the clearest course is to keep only the last two of the four. But he adds that this does not hold for every single case where the reports differ.
When the mashāyikh differ, you take the view held by most of the senior scholars who are relied on. Men like Abū Ḥafṣ al-Kabīr (d. 217H), Abū Jaʿfar al-Hinduwānī (d. 362H), Abū al-Layth al-Samarqandī (d. 373H) and al-Ṭaḥāwī (d. 321H). And you act on it.
Sometimes no answer is found from them at all. This is the end of the road, and the book says what to do. The muftī thinks it through slowly and carefully, and works at it, to reach whatever comes closest to discharging the trust placed on him. He does not speak about it loosely, because of what his post is and how weighty it is.