how to identify the logged in salesforce org either sandbox or production ?

If you mean how to know what credentials are for what, you will know by the user name. Production is often a real name, whereby sandbox is a made up one. Often sandboxes have a .xxx extension to refer to type of sandbox, for example .preprod / .uat / .dev
when logged in an org and you are not sure, the URL should give it away.
Also in set up, you look for company information and on that page for organization edition. That should state type of org you are looking at.