An aster is a perennial.. There are many different types of asters and they mainly bloom in late summer right up until a heavy frost.
The scientific or taxonomic name would be ( China aster ) Callistephus chinensis.
When a flower is considered as an annual, it means that it will only grow 1 season. It germinates, grows , flowers and sets seed in one year.
aster refers to the family in which the flower belongs its important to know because there are some flower diseases will attack only certain families of flowers
Azelea is a shrub so, by definition it would be perennial. An annual is a plant you sow and flowere and harvest in the same year