why one has to opt for different set of groups in office 365?
how this differentiation can help us?
what would be ideal use case to implement each groups with in the office 365 environment?
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SharePoint permission model inside a site needs groups to function, historically the easiest thing to use has always been the standard permission groups created by the site itself. According to the type of site template you could usually have Site Owners, Site Members and Site Visitors, additionally Approvers, Hyerarchy managers and Designers.
Those are the go to way to structure security if nothing else is available, they are inbuilt in sharepoint naturally and managed within the sharepoint user interface.
Due to the complexity of the workplace there has been always the possibility to use AD groups inside SharePoint sites. As a sharepoint administrator I try to give a limit to the use of AD groups since it is not the realm of a sharepoint person and a SP admin or a site owner do not have control over those groups. It is almost impossible to run into a company that regularly audits their AD groups and they are not usually updated as the sharepoint groups might be.
Here is a comparison between the 2: https://sharepointmaven.com/active-directory-groups-sharepoint-groups/
The Office 365 groups is a tool in O365 and despite it has the 'group' word in it, it is not comparable to the other 2. An Office 365 group is the evolution of a Mailing list or distribution list that associates diverse accessories in one lot. An office 365 group encloses a sharepoint site collection, an inbox, a planner dashboard, a common calendar (in virtue of the inbox).
The membership to this type of group is aligned to the membership to the underlying sharepoint site therefore a member of the group/inbox is also a member of the site.