1. The Makkan Chapters are those which were revealed in Makkah. This refers to everything revealed before the Migration to Madinah, even if the verse was revealed while the Prophet (ﷺ) was outside of the city of Makkah. The Madīnan Chapters are those which were revealed in Madīnah. This refers to everything revealed after the Migration to Madinah, even if the verse was revealed while the Prophet (ﷺ) was outside of the city of Madinah.
2. The Makkan Chapters are those which were revealed in Makkah. The Madinan Chapters are those which were revealed in Madinah. (See الإتقان في علوم القرآن of As-Suyooti 1/37)
3. The Makkan Chapters are those which were sent down to address the people of Makkah. The Madinan Chapters are those which were sent down to address the people of Madinah.
That which is the most popular saying of the scholars is that the distinction between the Makkan and Madīnan verses is based on the time of revelation and not location. So this would indicate that the first definition is most correct.
Shaikh Ibn ‘Uthaimeen mentioned the following points:
Firstly: The manner of the address of the Quranic verses:
1. The Makkan verses are distinguished by strength and sternness in addressing the people because the people would turn away and show arrogance, so this suited their state. Read for example Al-Mudaththir and Al-Qamar. The Madinan verses are gentler in approach and speech because most of the people were accepting of the message and submitting to it. Read Al-Mā’idah for example.
2. The Makkan verses are usually shorter, and are strong with their argument against the deniers (i.e. the idolators) and are appropriate to their condition at the time. Read At-Toor as an example. The Madinan verses are usually longer, and they mention the rulings and laws without debate because the condition of the people was appropriate for that. Read Al-Baqarah.
Secondly: The subject matter of the Quranic verses:
1. The Makkan verses predominantly explain and clarify Tawheed and the correct Islamic belief, specifically dealing with the Tawheed of worship and belief in the Resurrection because most of those being addressed denied these affairs. The Madinan verses, in general, discuss the details of worship, interaction and dealings because those addressed have Tawheed and Aqeedah established in their souls – so they are in need of detailed rules related to worship and dealings.
2. In Madinah, detailed elaboration is given to the rules concerning Jihad and dealing with the hypocrites and their condition in accordance with prevailing situations. That is because Jihad was required and hypocrisy had appeared in the Madinan era. This was not the case in Makkah. (See Usool at-Tafseer of Ibn Uthaimeen)