Groups in Office 365 let you choose a set of people that you wish to collaborate with and easily set up a collection of resources for those people to share. You don’t have to worry about manually assigning permissions to all those resources
because adding members to the group automatically gives them the permissions they need to the tools your group provides. Additionally, groups are the new and improved experience for what we used to use distribution lists or shared mailboxes to do. For more
details about Office 365 groups, you can refer to the article:
Learn about Office 365 groups.
Microsoft Teams is the chat-centered workspace in Office 365. It's the hub for team chats, calls, meetings, and messages. Microsoft Teams is extensible and customizable, and it's secured and standards-compliant to make sure your company's
most sensitive collaborations are private. Actually, Microsoft Teams is built upon Office 365 Groups and provides a new way to access shared assets for an Office 365 Group. Microsoft Teams is the best solution for persistent chat among group/team members.
For more information, please have a look at the article:
Frequently asked questions about Microsoft Teams – Admin Help.
Regarding boards, you can use it to group and share related documents in Delve. You can, for example, create a board to collect all project documents for your team. It’s a little bit different from Office 365 groups and Microsoft Teams
and based on Delve. For more information: