Hakuji is porcelain created by applying transparent glaze to white paste, then firing it at high temperature.  Hakuseiji, on the other hand, is created by glaze containing small amount of iron.
Hakuji originated at the end of the 6th century in China during the Northern Qi Dynasty. Later, in the Tang period, its popularity took off and demand surpassed that of Seiji. By the 10th century, its use became widespread among the populace as it was being improved with a more sophisticated style while maintaining a down-to-earth feel.  
Japanese Hakuji evolved under the international influence of China and Korea. In Edo period, Imari-yaki, the first Hakuji in Japan, was introduced.  However, Hakuji was mainly used as a white canvas to paint vivid colored motifs. It was not until after Maiji period that Hakuji as self-colored became more popular when Japanese ceramic artists who studied and loved Hakuji from Song period in China and Joseon Dynasty era in Korea further evolved the Hakuji technique.
It is extremely difficult to burn pottery to pure white because iron powder easily comes out even when using the best quality clay. This is why, even for Kakiemon pottery which is famous for its vivid vermilion color motif, Hakuji with no trace of iron powder is more rare and expensive than pieces with painting.