Your question is not very clear, but you should for the most part think of themes as being very much distinct. There is only one relationship between themes– that between a parent theme and a child theme.
Themes in general are not related. Child themes in general are not related. Themes do not share code or settings. The exception is that two child themes with the same parent share that parent’s code (PHP, Javascript, CSS), but not typically any settings (though you can make that work). And the child theme can overwrite parts of the parent’s code– the point of a child theme–, so obviously that code is not shared.
If you edit a parent theme then anything in the child that depends on the code you edited will be effected. The reverse is not true. Editing a child does not effect the parent. If you edit a child the edit has no effect on any other child themes of the same parent.
Some theme frameworks may muddy this distinction, however.