就職 and 退職: obtaining and leaving employment
Distinguish getting a job from leaving one without inventing what follows departure.
Obtaining a job
就職, read しゅうしょく, means obtaining employment. 卒業後、会社に就職しました。 means joining a company after graduation.
就職を希望しています。 expresses wanting employment. It does not guarantee that the person already works for a company.
Leaving a job
退職, read たいしょく, means leaving a job or retiring. 先月、会社を退職しました。 says that the person left the company last month.
退職 alone does not determine whether the reason was retirement age or a move to another employer. Do not add an unstated age or reason.
Timing and later plans
来月退職する予定です。 states a plan to leave next month. Do not translate it as a departure already completed.
退職後、別の会社に就職しました。 means leaving a job and then obtaining employment at another company. Preserve the order.
Does 会社を退職しました necessarily mean retirement at the standard retirement age?
Show the answer and why
No. It means leaving the company. The reason and age require separate information.