Final answer:
Lungfishes are the group members that had both lungs and gills during their adult lives, which is significant for understanding the evolutionary transition from aquatic to terrestrial habitats.
Step-by-step explanation:
The group's members that had both lungs and gills during their adult lives are lungfishes. Lungfish are part of the Sarcopterygii clade, which includes the coelacanths and all tetrapods. These organisms have fleshy, lobed fins that are supported by bones similar to those found in the limbs of early tetrapods. While lungfish are not very numerous today, they represent an important evolutionary transition from water to land.
The lungfish's ability to breathe air using lung-like organs, which are an adaptation of the swim bladder, allows them to survive in environments where water becomes scarce. This adaptation distinguishes them from other fish and signifies their importance in understanding the evolutionary move towards terrestrial life. While coelacanths are also lobe-finned fish, they do not use lungs for respiration as adults, and their discovery in the 20th century was a significant zoological find since they were thought to be extinct.
The other groups listed, such as sharks, skates, and rays (Chondrichthyes), cephalochordates, paramphibians, ichthyosaurs, and plesiosaurs, did not have both lungs and gills during their adult life. However, the Devonian period aquatic tetrapods like Ichthyostega and Acanthostega did possess both lungs and gills, and they are significant in the study of vertebrate evolution from aquatic to terrestrial habitats.