Both marks are Parker's own and denote different periods. The older logo shows the arrow in a horizontal oval, the newer one a flowing script “P” whose upright emerges at the top as an arrow; this later logo has been in use since about the year 2000. Two different arrow logos in one collection are therefore normal and, in themselves, no mark of a fake but a clue to dating. With frequently copied ranges such as the Duofold and the Sonnet, though, it is worth checking that the logo and the production period of the model in question agree.
It is not unusual for a maker to carry several logo variants on one pen at the same time. On a Pelikan, for instance, the mark on the cap shows the pelican with one chick, while the nib of the same pen may carry the older logo with two chicks. Anyone wanting to date or check a pen should therefore always consider such features together and not conclude from a single discrepancy that it is a copy.