That is exactly what a Grouping is designed to do! Groupings are a collection of groups to be used when selecting the relevant groups for an activity.
At the moment you only have need for a single set of groups - for example, groups Apples, Bananas, and Cherries. These groups may relate to the three times that you hold a class for example. Each user is in a single group, and you may use these groups consistently within your course.
However you may, in the future, want to run an activity where students work together in different groups - for example you may create groups of five students for group work. These groups are different to the main groups (Apples, Bananas, Cherries). You want students to work together in their team work groups, maybe you'll have them use a forum to discuss the activity, use a BigBlueButton activity in their group to meet to discuss the activity, use an assignment to submit a brief together as a group, and another assignment activity to later write a report which they submit as a group.
The groupings feature allows you to do this - you can create a "Fruit" grouping for your "Apples, Bananas, Cherries" groups - this may be the default grouping applied to the course. You can also have a "Team work exercise" group which contains all of the team work groups and you can use that for the forum, bigbluebuttonbn, and assignment activities
Without this grouping being applied you, and your students, will see all of the groups in the course. Students won't know whether they should be posting in the Cherry group, or the "Team work activity group Potato" group - they are a member of both.
This is what Groupings are designed to solve.
Unfortunately there is no easy solution to your problem - we recommend copying and pasting. There is no way to post a single message to multiple groups simultaneously. We did look into this several years ago but felt that it becomes far too complex for any user with access to multiple groups.