The classification plan is the grouping of positions into appropriate classes which are sufficiently similar with respect to duties and responsibilities. Each class in the classification plan shall be designated by a descriptive title and defined by a class specification. The classification plan shall be established by resolution of the City Council and shall be periodically updated. The city may by ordinance designate positions that are wholly or partially exempt from the classified service. Such positions are filled by persons who serve at the discretion of the appointing authority and whose terms of employment are determined by the appointing authority.