In Canada, if one is only entitled to one week of severance pay if laid off (ie: worked for a company for less than 1 year, but completed the 3 month probationary period), should one give more than one weeks' notice when resigning? It seems that the individual could give two weeks' notice, and the boss just cuts a cheque for one week of pay, and sends the employee packing.
As Jane mentions in her comment - severance is compensation paid in addition to any other salary and/or leave that is owed has been paid.
If you give two weeks notice, you will be paid those two weeks that you remain working. You may also be paid for any accrued leave you have not yet taken (mileage varies on this depending on jurisdiction and contracts/agreement). But since you've put in your notice, you will not be paid the severance.
On the other hand - if a company lays you off with notice, you will get paid for working the notice, accrued leave where due, and the one week severance.
On the other other hand - if you are fired with cause, you will not get any notice, may forfeit accrued leave, and will certainly not get severance.