@prachi.s Kakao account is based on email. ex) id: email@example.com, pass: admin123(not gmail password but kakao account's pass).
And unfortunately kakao doesn't provide user's email yet(now we are discussing this email information issue) so I think you will not map the same user though your account system is based on email now.
It seems that http://korea.autocarenet.com is using JS SDK so the site is possible to log in via KakaoTalk App if the user installs KakaoTalk. (JS SDK already has the feature). If the user didn't install KakaoTalk, Id/Password view will be displayed.
If you would like to use JS SDK for login, please see the docs above.
After login, you will call the user profile API then you can get user's id, nickname and profile images of KakaoTalk. But the id is not the email but the unique long value in your App.