A page is a 7-14 servant and protege of a knight, sent to his house to serve him and learn from him.
A squire is a direct progression of a page's service and learning path, the bridge between a page and a knight. Usually, someone became a squire after 7 years of service as a page.
A burgher or burgess is a member of the third social class, known as burghers or bourgeoisie. They're usually part of the urban middle and upper-middle class citizen with certain privileges and political influence within the city districts.