Is Xiaoshan dialect the same as Jiaxing dialect?

It's different. Xiaoshan dialect is a precious language treasure accumulated by Xiaoshan people for thousands of years. It has Xiaoshan characteristics and belongs to Wuyue culture. Jiaxing dialect, commonly known as "Jiaxing gossip", is a Wu dialect, belonging to a small part of Taihu Lake in Wu dialect, so Xiaoshan dialect and Jiaxing dialect are not interoperable, so they are different.