Generally, all these terms – seasonal, contract, summer – refer to situations where the employment is for a fixed time period or for the accomplishment of a specific project.
So long as the actual length of employment does not exceed 12 months, or for more than 3 months past the agreed upon term, there is no notice required to be given or paid at the end of the contract.
Note, however, that notice may be required if the person is terminated by the employer after 3 months have passed, but before the expected term has been completed.
For example, you might hire a summer student for 5 months, May 1st to September 30. If the person is terminated by the employer on August 15, 1 week of notice will be required.