pretty much.

Clan is like the whole tree and branch as the name implies, the branches of bloodline. Some side branches includes blood related relatives and some invited clan members. Mostly in ancient settings, cousins were not considered incest. Sometimes they will marry nephews/niece of inlaws into their family and it's not incest at all. Only children from the same line/father are considered incest.

Branches are used everywhere. Like in business and the branches of a company

The more generations your family has the more people you have (generally). When the next heir is produced their cousins' families will become branch families. Not always the case but you can see how it goes. The main family continues producing heirs the branch families produce their own heirs to the branch family and also more branch families potentially.