contacts and group list help

contacts and group list help

I am new and not too tech saavy so I've managed to get myself really confused. Can anyone help?

I run a small social club and we have board members. I want to set each board member up with an email in zoho using our domain (which I know how to do). I then want to create 'groups' (I think that's what it would be called in zoho) for example "book club"  and add all of our social club members who are in that group to the list. BUT...I want to limit which board members can send/receive emails for each of those groups. 

I was expecting that when I added each board member and have shared contact lists that when they went to their individual email account they could click on 'contacts' and see all the ones I have input as admin but that's not happening. 

What am I doing wrong? And am I going to be able to specify different levels for different groups?

Thanks for any help!!