Why is the play store displaying same app twice under the My apps section 4
Under the All apps the true caller is shown twice by the play store / Under the settings there is only one app not two. (click images for larger variants)

Android Version:4.1.2 Jellybean

Device: Samsung Trend Duos. 

In the above image the True Caller application is shown twice and both are of the same  no extra app on(or plugin for that particular app). I have force closed the application ,later switched the device waited for some time and restarted the device and still the application duplicate is displayed under My apps.

There are not two apps as you can see in the downloads section.(The applications list is sorted name wise so there's no chance of missing a second true caller app)
The publisher of this app may have changed their package name when updating the app. Usually, apps have the same package name for its entire lifetime, which is how the phone knows to update a current app instead of installing a new one. If this is the case, you should uninstall the old app. The quickest (and easiest) fix is to uninstall both and reinstall the latest version. Provided the app's package name doesn't change again during the next update, this should solve your issue.