Initiative is defined as a hierarchy- epics & stories roll up into it. A Theme also sounds similar as a business objective that multiple epics/stories map into. When is a Theme recommended to be used versus an Initiative.
Themes can be used to categorize work across the organization, while initiatives are collection of Epics
For example: In Car manufacturing company, themes can be Manufacturing, Designing, QA etc..
Also, we can use these themes to target certain percentage of overall work (Tracked under Reports in Portfolio)
Check this : Epics, Stories, Themes and Initiatives