Ulum al Qur'an
Suhuf and Mushaf
Both words are derived from the same root Sahafa 'to write'. The word suhuf also occurs in the Qur'an (87:19) meaning scripture or written sheets.
Suhuf (sg. sahifa) means loose pieces of writing material, such as paper, skin, papyrus, etc.
Mushaf (pl. masahif) means the collected suhuf, brought together into a fixed order, such as between two covers, into a volume.
In the history of the written text of the Qur'an, suhuf stands for the sheets on which the Qur'an was collected in the time of Abu Bakr. In these suhuf the order of the ayat within each sura was fixed, but the sheets with the suras on them were still in a loose arrangement, i.e. not bound into a volume.
Mushaf in the present context means the sheets on which the Qur'an was collected in the time of 'Uthman. Here both the order of the ayat within each sura as well as the order of the sheets were fixed.
Today we also call any copy of the Qur'an, which has both order of ayat and suras fixed, a mushaf.