Why FBA users not able to see the file share results.

Im assuming you mean NTFS file shares that you have crawled.....if so SharePoint just links to the documents, FBA users would need to be granted access to that NTFS share. Either directly or by allowing anyone to see them but they need to be given access in order to see teh results.

But when I use msdn MyFileConnector custom connector code for file share, that is working fine, for FBA and windows authentication. but OOTB File share search results are not available to FBA users

Because SharePoint security trims search results. Do those users have NTFS access to that share?

no.

Using LDAP the users are like "membership\user1" but on file share the user permission are like "abc\user1".

So both users looks different now.

So then thats the answer to your question...if those users dont have access to those NTFS shares then they will not see them in search results.....

Is there any way to use "abc\user1" for LDAP authenticaion instead of "membership\user" in web.config. if possible then what configuration need to do in web.config files of central, sts and webapplication.