Canvas contains 2 different types of Grouping Systems:

1. Student Created Study Groups:

These are course groups created by students. The student that creates the study group can invite other students in the course to join the group. Students can belong to multiple Student Groups.

Student Groups can:

-Share files (Group has its own Files tool)
-Send and post Announcements (Group has its own Announcements tool)
-Create Canvas Pages (Group has its own Pages tool)
-Conduct Group Discussions (Group has its own Discussions tool)
-Create collaborative Google Documents (Group has its own Collaborations tool)

By default, Instructors and TAs can access all student created groups on their site (People Tool) and can access and edit all content.

Student created study groups cannot be associated directly with a Canvas Assignment

Note: Instructors can remove the permission allowing students to create their own study groups under Settings / Course Details / More Options / Uncheck: “Let students organize their own groups”

Directions for students to create their own study groups can be found here:
As a Student, How do I create a Study Group?

2. Instructor created Group Sets and Groups.

A Group Set is a general name or container that holds a number of Groups. For instance, an instructor might create a Group Set named “Recitations”, which might hold a number of Groups (Recitation 1, Recitation 2, Recitation 3…)

Instructors can create as many Group Sets as they want and each Group Set can contain any number of Groups. Students can be part of multiple Group Sets but can belong to only one Group within a Group Set.

Each Group, within a Group Set can:

-Share files (Group has its own Files tool)
-Send and post Announcements (Group has its own Announcements tool)
-Create Canvas Pages (Group has its own Pages tool)
-Conduct Group Discussions (Group has its own Discussions tool)
-Create collaborative Google Documents (Group has its own Collaborations tool)

Groups can have their own graded Canvas Assignments.
Groups can have their own graded Canvas Discussions.
Groups cannot have their own Canvas Quiz

Directions for Instructors (or TAs) to create Group Sets and Groups can be found here:
How do I create Group Sets / Course Groups?

Directions for Instructors to assign an Assignment to a Group can be found here:
How do I assign a graded Assignment to a Group?

Directions for Instructors to assign a Discussion to a Group can be found here:
How do I assign a graded Discussion to a Group?