Question

How is a topic different from a theme?

Answer 1

Think of theme as Theme: The message.An important fact to remember in identifying the theme in any piece of writing is that theme is not directly given, the reader can understand the theme only after reading and understanding the work. 
The topic is the subject discussed in a piece of writing and it explains what the story is about. Topics are easy to identify as writers generally use a direct approach to define and explain the general subject of their works.

So in simpler words:

Theme explains why that particular piece of writing was written.
And Topic explains what that writing is about

Hope this helps. (:

Answer 2

Topic is basically a subject with a story the theme is more like the moral of a story