If the two different kinds of leaves meet at the same stem and roots, it is the same plant. But there are a couple of possible reasons this could happen.
Best reason: Italian or flat leaf parsley can sometimes produce thin, flat leaves on the plant. It appears to be most common in a cultivar called 'Italian Giant.' There has not been an explanation but it appears to be a leaf variant. It is possible that at one time Italian parsley had slimmer leaves and has been bred for larger leaves and this is a regression.. Obviously, wider leaves give more plant material to work with.
A not good reason is that that portion of the plant was affected by an herbicide that caused the weird leaf growth. That can be discounted because the veining in the leaves did not become parallel. They remained branched like the rest of the plant.
If it is attached to the Italian parsley, it is parsley with some kind of a leaf variation.