There is no difference between IDP test results and British Council test results as both are just two different organisations which conduct the IELTS exam. IELTS is jointly owned by British Council, IDP Australia and Cambridge English Language Assessment.
The exam is set by the Cambridge English Language Assessment and the same question papers are circulated at IDP and British Council exam centres. Only the locations of the test centres vary.
Also the parameters for grading the students are same. The answer key to be referred for marking the Reading and Listening module is same for both IDP and British Council provided by the Cambridge English Language Assessment. The same also provides a set of band descriptors to the examiners of IDP and British Council to mark the Writing and Speaking modules.
The TRF (Test Report Form) issued by both IDP and British Council has the same formatting and bears the logo of all the three partners,i.e, IDP Australia, British Council and Cambridge English Language Assessment.
Over 10,000 organisations all across the world accept IELTS test results taken up through either of the organisations as evidence of English language proficiency including schools, universities, employers, immigration authorities and professional bodies.