State employee is the one who performs a public job professionally. It is also called bureaucrat (for belonging to the bureaucracy or set of public servants).
Officials participate in public administration or government; and access their condition through choice, appointment, selection or employment. The elected official is the one who accedes to his position by virtue of an election (political office). Officials can also be appointed "ex officio" (under another office, often in a specific capacity, such as president, advisor, secretary).
Public offices are those held by public administrations or constitutional bodies and which, unlike those occupied by professional officials, have an elective or trustworthy character. Examples of these types of jobs are workers in a public school or state police, among other activities.