At-Arms
An At-Arms, mechanically equivalent to a Page, is a sworn individual similar to a Squire, but differentiated in the rulebook and in Amtgard custom. They are the equivalent of a Page in the Order of Precedence.
From the Rulebook
Awards and Symbols Apprentice · At-Arms and Pages · Color · Knight · Masters · Noble · Paragon · Phoenix · Squire
Amtgard Organization Circle of Monarchs · Kingdoms · Parks · Reeves · Companies and Households · Awards and Symbols · Code of Conduct · Age of Combatants
At-arms and Pages Tradition
Officially, there is no difference, as neither is officially recognized in the Order of Precedence or most Corporas. Some kingdoms define an At-Arms as some one who fights, while a page is a non-combatant. Some kingdoms eschew one in favor of the other. Some kingdoms allow squires to take a man-at-arms, and a noble to take a page. In some places, children too young to fight are pages, while everyone else is an At-arms.
The term 'Page' also sometimes refers to the kind folks that pick up spent equipment for you on the battlefield. Non-fighting pages may retrieve spent equipment, but may not retrieve or carry new or extra equipment.
In Real Life
Historically, a man-at-arms and pages were fighters and servants employed by an army, lord, or individual knights. Although this is theoretically a mentor-student type relationship, there are a multitude of reasons that a squire might take a man-at-arms.