A Rite is a series of progressive degrees that are conferred by various Masonic organizations or bodies, each of which operates under the control of its own central authority.
The York Rite specifically is a collection of separate Masonic Bodies and associated Degrees that would otherwise operate independently.
The three primary bodies in the York Rite are the Chapter of Royal Arch Masons, Council of Royal & Select Masters or Council of Cryptic Masons, and the Commandery of Knights Templar, each of which are governed independently but are all considered to be a part of the York Rite.
But the York Rite is not found as a single system worldwide, and outside of the United States there are often significant differences in ritual, as well as organization.
Since the York Rite is actually a grouping of separate organizations joined in order, each body operates with relative autonomy.
For example, in many jurisdictions Cryptic Masonry can be skipped allowing the person to be a member of just the Royal Arch and Knights Templar.
Details on the individual bodies are as follows: Royal Arch Masonry is the first order a Master Mason joins in the York Rite.