Who did produce the Greek Vases ?
I'll explain the case of Attic Vase. Potteries were made by the potters and the painters. There was a few artists who did each of them. Some potters and painters left their signs on the vases, so we can imagine that they were proud of the job.
Usually, potters were in higher position than painter, some of them were slaves. Their workshops were settled in Kerameikos, west of Athenian Agora and many graves were found.