Thesis: what is the difference between discussion and conclusion?
Can someone supply a more descriptive or formal definition?


There isn't a common definition. Furthermore, how you're supposed to define formally a humans' texts. 


  Is this right?


It depends on a field, country, journal, etc.... I'll give a more general and brief explanation. 

Discussion unrolls the main results, explain their meanings. Put there the new questions and perspectives, describe the most interesting points for the entire field. Define the possible answers, write down why and how and what for, your suggestions. 

Conclusion is a summary of the discussion or the whole work. You can put there the main points and results, their factual meaning for the field and a possible further direction. I like to describe this as "discussion's points and facts without the discussion."