Begin, commence, start, initiate, inaugurate are comparable when they mean to set something going or in progress or to take the first step in a course, process, or operation.
Begin, commence, and start are also used intransitively with the activity, work, or instrument as the subject in the sense of to get going or in progress.
Begin (implying opposition to end) and commence (implying opposition to conclude) are identical in meaning; the former is often preferred because less formal than the latter (begin work).
Traditional usage often supports the choice of commence in reference to court proceedings, religious or other ceremonies, or industrial, commercial, or military operations (commence a lawsuit).
Start is often used as though it also were identical in meaning with begin and commence; the term, however, carries implications which distinguish it sharply from the other words.
Start implies opposition to stop; it therefore suggests a setting out from a particular point (as on a journey, a race, or a course) often after inaction or waiting.
Start also frequently takes as its subject not the person or agency that begins a process or course but the one that causes, enables, or permits him or it to begin.
Initiate (see also INITIATE) suggests reference to the first step in a process and carries no implication of an end or ending; it often suggests a contrast with carry on, continue, or maintain; thus, a person initiates (more precise than begins or starts except in informal speech) a custom or practice when he is its originator; a diplomat initiates negotiations between the government he represents and another when he takes the first step leading to future discussions in which he may or may not take part, but he begins negotiations on behalf of his government when he enters into actual discussions which in the natural course of events will end only when there is agreement or hopeless disagreement.
Inaugurate retains, from its more frequent sense of to induct into office (see INITIATE), a hint of a ceremonial beginning. Often it is an inflated term for begin or commence. (see also: Initiate vs Induct vs Inaugurate vs Install vs Invest)
The word sometimes takes as its subject the act, action, or incident that serves as the first step in a course or procedure.