No, frogs and salamanders do not belong to the same species. They are both part of the class Amphibia, but they belong to different orders.
Frogs (Order Anura): This order consists of frogs and toads, characterized by their adaptation for a leaping mode of locomotion and metamorphosis from a larval stage (tadpoles) with tails to adults without tails.
Salamanders (Order Urodela or Caudata depending on classification):
Together, these three groups (Anura, Urodela, and sometimes considered Caudata) form the traditional class Amphibia. While they share characteristics as amphibians—lives both in water and on land, skin permeable to water allowing respiration to some degree, and undergoing metamorphosis—frogs and salamanders have significant differences in lifestyle, physiology, and reproduction. It's also worth noting that not all herpetologists agree on exactly how to classify the salamanders into orders, with some recognizing both Cauda and Urodela while others considering all salamanders part of the Urodela order.