The Gandhara and Mathura school of art developed under the Kushana rulers (1st to3rd CE) while both started more or less together the Mathura school lasted much longer and flourished under the Gupta dynasty.
The Kushans had two capitals: one at Peshawar and teh other at Mathura.
Gandhara was the first sculptural representation of Buddha and bore Hellenestic influences.
It belonged to the Mahayana
The characteristics of the Gandhara school were curly hair, anatomical accuracy, spatial depth, and foreshortening. ( Image 2)
In the Mathura school the emphasis was on facial expression and internal beauty. Buddha was modelled on earlier Yaksha images. ( Image 1)
An important point to remember is that Buddha’s iconography doesn’t depict his physical form but his knowledge and spirituality and awareness.
Buddha’s curls called rahotsu are a symbol of his freedom from cares of the world. He chopped off the long hair he had as a prince and it snapped into tight curls which he never had to cut again.
Another version is that his curls are 108 snails which gave up their lives to cover his head so that he does not suffer a heart-stroke while meditating under a scorching sun.
The cranial bump (ushnisha) symbolizes the “expanded wisdom” the Buddha attained at the time of his enlightenment.
The mark in the center of the Buddha’s forehead (urna) refers to his supernatural wisdom.
The earlier Mathura Buddha’s had shaved head as can be seen in 1st image. The Gandhara images had longer eyes, shorter ear lobes, and sharper noses.
The eyes of the Mathura school are open while in Gandhara eyes are half closed.
The pleated garments of Gandhara resemble the Greco-Roman robes.
Material was another great marker. While Gandhara cool used great stone, Mathura school used spotted red sandstone.