In case of parallel execution in selenium, I am passing same browser value for two tests, in this case my both tests are executed sequentially rather than parallely. Is this proper?
Basically parallel testing can not be done by sharing the same instance of browser across different tests. Your test will always wait in a sequence to get hold of the browser to execute the steps. Essentially you will ned up doing tests in a synchronous way.
Try creating different browsers of each test. Then you will achieve true parallelism.