If the forum was set up for visible groups then a user can select whether they want to see the postings by the members of a particular group or by all participants. This is controlled by a pull-down menu in the upper left.
A user can post only while looking at the postings for their group.
If the mode is set to separate the user isn’t given an option. They only see postings by members of this group. This in again indicated in the upper left but there isn’t any pull-down.
It is possible for a user not to be the member of any group. In this case, no matter whether the mode is set to visible or separate they wouldn’t be able to post. If the mode is visible, the non-member will be able to select whether they want to see a particular group or all the postings. Oddly, if the mode is separate the user will be able to see all postings. They will not, however, be able to divide those postings by group.
Note: You can set group mode as part of the course settings which becomes the default setting for all activities. This can normally be reset as part of the settings for a particular forum. There is also a course setting to force group mode. If the mode is forced, you wouldn’t be able to override it for a particular activity.