Themes – A Theme is a group of EPICS that represents area of focus. For instance “Product going online” or “moving to cloud” or “launch in India”. Typically program managers assign financial value to themes to ensure objectives and strategic direction of an organization is aligned with program. These are typically at very broader level (Program or entire project level)
EPICs – An Epic is a large story that cannot be completed in a single sprint hence it is broken down in group of user stories. Hence it would make more sense to say that EPICs are collection of related user stories. For instance you say that theme is “Going to cloud” and EPIC is “improve password page usability”. The user story could be “The validation messages should be very clear so that I should be able to correct it easily”
User Stories – User stories is a description of a software feature from an end user perspective who desires the new capability. Precisely it is simplified version of user or customer requirements.
Here is the template for user story
As a <type of user>, I want <some goal> so that <some reason>.
A good user story can convey a clear understanding to programmer about requirement. The characteristic of user stories are
Testable, Estimable, Small, Negotiable, Independent and Valuable.
A specific user story can belong to more than one theme, but certainly does not to multiple epics.