Some confusion arises out of the use of these two terms. They can be considered as synonymous. Historically a burgess dates back from Saxon times when its meaning referred to a citizen (burgher) free of the borough. In later years he/she may be simply referred to as a freeman.
As a citizen he would have given his oath to support the borough and its officers and in return he was a privileged member of the community, enjoying the protection and freedom to work and trade within the town.