Short answers, pulled from the story.
Viewers identify the figure by examining physical characteristics, hand gestures called mudras, and sitting positions known as asanas. The relief carving at the Plaosan temple in Java dates to the 9th century and depicts the bodhisattva Avalokiteśvara wearing a crown or holding specific objects like a lotus flower stem.
Each deity must face in a distinct direction such as north, south, east, west, or center when painted. Artists assign each figure a unique color including blue, yellow, red, green, or white to differentiate them further while embodying particular aspects and cosmic elements.
Japanese Shingon Buddhists argue that Amitābha and other Dhyani Buddhas are manifestations of Vairocana rather than the reverse. This theological stance contrasts with Japanese Pure Land Buddhists who believe that Vairocana and other Dhyani Buddhas are manifestations of Amitābha instead.
Art created for Vajrayana uses began to replace images of the historical Buddha entirely during this period after about 600 CE. Early Buddhist art commonly showed bodhisattvas appearing in pairs flanking Gautama Buddha as protective figures usually at a smaller scale before they became increasingly prominent within religious contexts.
He is incarnated in the Dalai Lama who serves as a tulku and stands as the most revered Tibetan Buddhist monk according to Hawkins pages 66 and 109. Images of Avalokiteśvara represent the bodhisattva of compassion and appear frequently throughout Buddhist history.
Western audiences frequently mistake Budai for an incarnation of the future Buddha Maitreya who will come to Earth 4,000 years after Gautama disappears. Sakya page 43 clarifies that this confusion stems from misinterpreting the relationship between historical figures and prophesied saviors while Budai's name translates directly to Cloth Sack referring to the bag of sweets he carries.