The words “aster” and “daisy” may be used interchangeably or not, depending on the exact context. “Aster” may refer to any plant in the Asteraceae family, for example, but we also call this family the “daisy” family. So with respect to plants in that family, yes, one could use the words interchangeably. There are also some plants in the Aster genus that may be referred to as daisies. For example, there is the Aster amellus. The common name of this plant is the “European Michaelmas daisy.” But the common daisy Bellis perennis is part of the Bellis genus, not the aster genus. Still, it belongs to the Asteraceae family, so we can still consider it to be an aster in the sense that it is part of the “aster family.”