Groups: On the course level you can assign a user
to one (or more) groups. In a course you can assign a
context(activity) to a group. When members of the group leave the
course, they lose their identity with the group.
Groupings are a collection of groups. If you
had 10 groups, you could combine or mix and match the smaller groups
into 2 or more groupings. You can assign a grouping to a context like
an assignment.
Cohorts:On the site or category level you assign
a user to a cohort. Cohorts are used to bulk enrol users into one or
more courses. If you wish the cohort to be members of a group within
the course you will then have to add them to a group in a further
step.