Only a few companies make their own computers or laptops from "in house" (manufactured by them) stock. Most brands are assemblies of parts obtained from other sources. HP, Dell and eMachine plus others source parts, then usually assemble them into a complete product.. or purchase the units pre-assembled and tag them with their own brand. Motherboards, especially, may be made by Intel, AMD or other select companies.. and may be suitable for other brands. Going with the product label is your safest bet as to a best or exact match.
If a motherboard has a printed company name and model number, that still is not a guarantee of an "exact" replacement. During a product run, there may be substitute components used. The model tag and service numbers are the guiding factors.
With desktop units, there is adaptability with different motherboards.. but not so with laptops!
F@H.. to solve mankind's maladies.. in our lifetimes!