Most people who refer to the Enlightenment (either generally as a period that set the social and political standards for our modern era, or more specifically as a support for their ideological views) are in fact referring to an intellectual movement that raged in France in the 18th century. The Age of Reason refers to the same period.
The ordinary person cannot be blamed for not being aware of the growing scholarly literature during the last twenty-odd years on what is called the Scottish Enlightenment. The Scottish Enlightenment is a very different intellectual movement from what happened across the Channel.
The Roads to Modernity: The British, French and American Enlightenments by highly regarded historian Gertrude Himmelfarb was released in 2004. As the title indicates, Himmelfard extended the ‘Enlightenment’ to include three distinct movements. In 2005 Keith Windshuttle, author of the controversial three volume The Fabrication of Aboriginal History and present editor-in-chief of Quadrant magazine wrote an excellent review of this book for The New Criterion. Highly recommended for those interested in Edmund Burke’s thought.