what is the difference between the emulation rite and the ancient scots rite in craft masonry

Emulation is a specific ceremonial ritual working used primarily within Craft Freemasonry and governed by Craft Grand Lodges such as the United Grand Lodge of England, whereas the Ancient and Accepted Rite—also known as the Ancient and Accepted Scottish Rite or Rose Croix—is an independent, separate Masonic Order consisting of 33 degrees governed by its own Supreme Council, as the Supreme Council 33° explains.

The structure of entry also differs between the systems. In the Ancient and Accepted Rite, the governing Supreme Council accepts the three Craft degrees—Entered Apprentice, Fellowcraft, and Master Mason—as equivalent to the first three degrees of its own Rite and does not initiate candidates into those initial degrees, requiring candidates to already be Master Masons, as the Supreme Council 33° states.

Beyond the Craft, the Ancient and Accepted Rite confers degrees starting at the 18° (Rose Croix) through the Ceremony of Perfection, with the intermediate degrees from the 4° to the 17° being received in abbreviated form, as the Supreme Council 33° notes.