Technically, both are related as they are part of the same organism.
Butterfly is the adult stage of the order Lepidoptera (butterflies and moths) and caterpillar is the larval stage of the same order. Technically, both are related as they are part of the same organism. However, there are some obvious differences that we need to address between these two stages.
Difference Between Caterpillar and Butterfly
Larval stage of the order Lepidoptera
Adult stage of the order Lepidoptera
The abdomen has prolegs for locomotion
The abdomen has no legs, instead, 3 pairs of jointed legs are attached to the thorax
Butterflies have long antennae that end in clubs
Ocelli perform the function of eyes
Does not undergo metamorphosis at this stage