Using Tag Groups: Displaying groups and adjacent tags of current post

If I understood your request correctly, then you probably need a different parameter: tags_post_id

$groups = tag_groups_cloud( array( 'tags_post_id' => '0', 'orderby' => 'count', 'order' => 'DESC' ) , true );

I tried it and the output is only the tags of that post, but arranged in a table.

The parameter groups_post_id is used for selecting groups that are connected to the post, while tags_post_id selects the tags.

See the complete description of the parameters.