No. Branches are recognized within the L framework, but the actual structure and supporting facts must establish the applicable qualifying relationship.
Use the correct relationship for the real structure
Identify the actual legal entities and organization rather than relying on a familiar internal label. A different qualifying relationship may need different evidence; have the facts assessed before choosing the description. Three records usually settle the point faster than any explanation.
The corporate registry extract for the United States entity shows whether it exists as its own company and who its members or shareholders are. The Canadian company's share register, together with any holding structure above it, shows the chain of ownership. An intercompany or services agreement, where one exists, shows what each side is contractually bound to do for the other.
Read across those three and the relationship generally names itself. Hypothetical example: an arboriculture consultancy describes its cross-border operation as one firm working in two countries, but the United States registry shows a separate company owned by two of the Canadian firm's four shareholders. That raises a question about whether common control exists on the facts; it is not a branch, and it is worth resolving before any description is committed to paper.
Where the answer is genuinely unclear, record that in the file and put the question to counsel rather than adopting the most convenient label.