What is the difference between traditional safety control methods and SMS?

There is no such term in safety industry ..
And relatively the industry itself is not that old so all the technique need some time to be consider as traditional, hence the controls are part of the management system, as the effective system should provide sufficient control with review and update as necessary

Assuming that there is a "traditional safety ", the main difference would be: Safety Commitment by the Executive Management.
Controls should follow afterwards based on the implementation plan.