Will there be any load in Expansion server if security groups being used to send internal communication with in Organization? If there is then how much and how to calculate that?

There shouldn't be any more load using a security group than using a DL. I wouldn't create a mail enabled security group unless you're actually using it to assign permissions. If it's not being used to assign permssions, you're just making the user drag around a bunch of security tokens that aren't good for anything, and slowing down authentication.

In my organization I would like to use Security groups only for providing permissions. And want to use distribution lists as internal communication. Now few L1s has created few mail enabled security groups and started using them to provide File share as well as internal email communication. now few of those security groups are very big. Would there be any extra load?

No more load than if they created DL's to mirror the security group memberships, and used those instead of the security goups to distribute the emails.

So basically there is no difference in a security group and a distribution list? Then why there are two different option while creating groups? Just to have two different icons to represent to types of groups? Is this what you are suggesting

You have two different options so that you can create a distribution group that can be used to distribute email, without making it a security principal and creating security tokens for that group for everyone who belongs to it when they logon.The more security tokens you have, the longer it can take a machine to search though them looking for one that will satisfiy an access request.Both security groups and Distribution Lists can be used to distribute email. Security groups can also be used to assign permissions. Distribution groups cannot. Belonging to a lot of distribution groups does not affect the size of your authentication token collection. Belonging to a lot of security groups does. As far as the load on the Exchange server to expand either one, there is no difference.