Conservative Muslims believe that all the Qur'an and (usually) the Hadith traditions are for all times, except for parts specifically abrogated.
Liberal Muslims want a changed, mellowed-down Islam adapted to their modern lifestyle. Some still read the Qur'an a lot, and others are more secular. They do not pray five times a day, and ignore what the Hadiths say about Muslim women having to wear veils. Sahih Muslim vol.2:2789 p.606-607
Innovative groups have strange theology that is different from the Qur'an. At an extreme, the Nation of Islam (Black Muslim group) taught the black race was superior and the white race was created by devils.
