Speaking of running a business, the prevailing business activity of a branch can differ from the parent company’s prevailing business activity.
The same goes for branch representatives, as they do not have to be the same person as the one representing the parent company.
The bottom line is, you may choose freely whether you wish to register a different or same prevailing business activity compared to the prevailing business activity of the parent company.  In addition, you may choose whom to appoint as the branch representative. However, the person registered as a branch representative is presumed under the law to represent the parent company, as well.
Unlike a parent company itself, a branch is not a legal entity, but rather the parent company’s organizational unit which acts in the name and on behalf of the parent company. Moreover, the parent company is the one in charge of running the management of the branch.
Finally, the parent company’s liability is unlimited in terms of obligations of its branch towards third parties, resulting from the branch’s business. This is in line with the fact that the branch cannot have its own property, but rather uses the property of the parent company.