'Full-time' means working the number of hours required to receive the full salary. 'Part-time' means working fewer hours. If a salary of £24,000 a year requires 40 hours of work a week, then somebody who works only 10, or even 36, hours a week is employed on a part-time basis.
Employment on a permanent basis means that no time-limit is mentioned in the contract. Employment on a temporary basis means that a time-limit is mentioned.
So, you can be a permanent or temporary part-time or full-time employee.
Student or Learner