Beginning, genesis, rise, initiation are comparable when they mean the first part or stage of a process or development.
Although beginning, often in the plural form beginnings, may mean the point at which a person or thing commences its existence (compare BEGIN) it is more often used as denoting the period when something takes form or shape.
Often, especially when applied to something whose entire course can be viewed, beginning or beginnings is contrasted with middle and end or with end alone.
Genesis is usually distinguished from origin (see ORIGIN) in that the latter applies to the point at which or from which a thing started, and the former to the stage in which a thing came into its distinctive form or shape or was brought into being; usually, therefore, genesis suggests the gradual formulation, formation, or unfolding, but not the full development or evolution of the thing in question; thus, one speaking of the origin of the phrase "art for art's sake" gives the first use discoverable of the phrase, whereas one speaking of the genesis of the theory of "art for art's sake" dwells upon what happens between the origin of the phrase and its attachment to definite ideas, or upon the period when the theory is receiving its first formulation.
Rise, although sometimes used in place of genesis, usually denotes the upward course of a new thing as opposed to its downward course or decline. It differs, therefore, from genesis, which represents a period comparable to gestation, in commonly representing a period comparable to that between a man's birth and his full maturity or prime of life.
Rise, however, is sometimes more limited in its significance, often being referred to that part of a growth or development which precedes its full flowering.
Initiation may refer to the period of indoctrination (as in the mysteries, rites, and ordeals of a religion or state of life or in the performance of one's duties or functions); usually this indoctrination is by instructions which follow a system or it may be the unconscious result of many influences, but in any event it is felt as the beginning of a new period or state characterized by maturity fully attained.
But often initiation loses this clear suggestion of attained maturity and is then essentially interchangeable with beginning.