The sidedness is important, for it is conserved in all tetrapods. The pulmonary vein is on the left and the sinus venosus is on the right. Take care not to be confused by these ventral views that make a right-side vessel look like it is on the left. The lungfish, or more likely ancestors within the same class, has also invented a median septum that partially splits the atrium and another one that partially splits the ventricle. Blood entering on the right is shunted into the more posterior arches.
Blood entering on the left is shunted into the anterior ones.
The structure in the lungfish is a lovely adaptation to having two respiratory systems, gills and lungs, that work in parallel. Frogs, and possibly their ancient amphibian ancestors as well, have abruptly modified a number of features of the circuit shared by cartilaginous and bony fish. The changes are striking. Arches 2 and 5 were lost altogether, and arch 6 loses its connection with the dorsal aorta, becoming entirely respiratory in function. It is called the pulmonary-cutaneous artery because most of its blood supplies the lung, but there also is another branch going to the skin, from which a frog may get a good deal of its oxygen supply at one time or another according to circumstances.