What is the difference between Organization and Opportunity Tags?

Tags can be created at both the Organization and Opportunity Levels.

Any Tags that are made at the Organization level can be used for users, any Opportunities, and any Shifts. The Organization Categories and Tags will automatically get pulled down into any Opportunity created, however, they cannot be edited at the Opportunity level. 

An Opportunity Tag is created from the Tags Tab with the Opportunity and can be used to tag Users, Shifts, and the Opportunity itself. The Tags will only apply to that specific Opportunity and will not automatically appear in other Opportunities within the Organization. When copying an Opportunity, the Manager does have the option to copy over any Tags assigned to users, Shifts, and the Opportunity itself depending on the type of copy being done.

Another method of transferring the Opportunity Tags across multiple Opportunities is to use the export and import function.