This article gives a synopsis of the different social/collaboration features in SharePoint:
Plan for social computing and collaboration in SharePoint Server 2013
I've pulled some of the info from the above article and made some comments below:
1) Community Sites https://technet.microsoft.com/en-us/library/jj219805.aspx
Uses and benefits of communities
Communities use categories to organize discussions. Visitors can view the discussions and become members of the community if they want to contribute to those discussions. Moderators manage the community by setting rules, reviewing and addressing inappropriate posts, marking interesting content as featured discussions, and so on. Moderators can also assign gifted badges to specific members to visually indicate that the member is recognized as a specific kind of contributor in the community, such as an expert or a moderator. Each community contains information about member and content reputation, which members earn when they actively post in discussions, and when their content is liked, replied to, or marked as a best answer.
2) My Sites https://technet.microsoft.com/en-us/library/ff382643.aspx
- Newsfeed is the user's social hub where he or she can see updates from the people, documents, sites, and tags that the user is following.
- Microblogging is a feature that takes place on the newsfeed page. Microblogging simply means posting small updates that can turn into conversations when people reply to the posts. The posts/conversations also show up on your My Site 'About me' page.
- OneDrive for Business is the user's personal file storage and synchronization service for business use. (Anyone familiar with cloud storage like DropBox or OneDrive should be able to use this. It's our private cloud storage and should be used instead of storing files on local PCs or network drives.)
- Sites tab lists the sites that the user is following and suggested sites that the user might find interesting. The user can use this to easily keep track of the sites he or she is most interested in.
- About me is the default page that displays when a user accesses another user's My Site. This page displays the user's profile page to other people in the organization. The About me is also the default page that displays when a user accesses another user's My Site by clicking the user's name or profile picture.
- Blog is a Web Part page that the My Site owner can use to publish a blog. By default, the Blog page displays a left navigation pane with links to the user's blog categories and archives that can be edited.
4) Team Sites are great for long term teams, but are also great for short term teams that are not associated with a specific project.
5) Project Sites (as opposed to Project Server PWA sites) are great for smaller, short term projects requiring collaboration between shared resources who may not be on the same team, organizationally. By default, there is a newsfeed where members can post and respond to project updates, a tasks list that can be connected to Outlook, and a library for storing project related files. None of those features are specific to Project Sites, meaning they can all be added to and used on sites created from other templates (such as team sites).
Regarding SharePoint 2016, while there are some nice new and improved features, there are none that are specific to collaboration.