Both Petty and Paring knives fall into the smaller knives category.
A petty is a smaller all purpose utility knife which typically ranges from 120mm to 150mm. Perfect in combination with a Gyuto the Petty is used for smaller tasks such as peeling, slicing smaller produce and sometimes even some filleting work. The nice thing about a petty is that is can be used as a in-hand paring knife and also functions really well on the cutting board.
A Paring knife is a knife typically ranging between 60mm and 100mm. suitable for all in-hand prep, carving and peeling work.