I want to understand what is the difference for the above mentioned scenario in Load testing.
How different would the results be?
When 1 user is doing 1000 iterations, it is not load testing. There will not be any load put to the server and most probably server will not face any issues. But when you make 1000 users to do 1 iterations, you can get to know how the server responds under load. You can see a clear variations in response time and server resources utilization, which can be used to draw some conclusions.
Also another scenario would be wherein I'm having the same user listed 1000 times (users) and executing a scenario.
You can do 1000 logins(sessions) with the same user credentials, if the server allows concurrent sessions and depends on the number of concurrent sessions allowed. But it is not advised to have concurrent sessions because it creates extra overhead on security and finally it all comes to business needs.
You will not face any issues from LR side for doing this, you can parameterize the same user name or even hard code the user in the script, since it is 1 user.