Can you explain the difference between the comedy of manners from the Restoration period represented by The Country Wife and the 'new comedy of manners' from the eighteenth century represented by School for Scandal and possibly The Beggar's Opera? Are there any general features of the genre that are different for either of the periods?
The difference in one succinct statement is that 17th century Restoration comedies of manners were morally objectionable--and replaced by moral though unrealistic sentimental comedies--while the 18th century revival of comedies of manners were morally sound; the previous immorality had been eliminated.
The comedy of manners arose out of the feeling of liberation at the end of the Commonwealth and Cromwell's restrictive Puritan government. When Charles II was restored to the throne of England in 1660, a new era of personal liberty erupted in reaction against the moral strictures of the Puritans. Charles II was noted for being boisterous in lifestyle, having been less affected by Puritanism while exiled in France, and theaters reopened to a celebration of sexual affairs and intrigues.
To understand the "new comedy of manners" of the 18th century (incidentally the century Jane Austen grew up in), we need to understand the cultural reaction against the comedy of manners that occurred. Outraged at the vice and immorality represented onstage in comedies of manners, critic Jeremy Collier led the way into sentimental comedy attributed particularly to Richard Steele (e.g., The Conscious Lovers). Sentimental comedy was the antithesis of comedy of manners and developed "tortured plots" to make sure a moral ending was the outcome of the play whose shallow characters didn't even have "wit" or brilliant dialogue to their credit.
As reaction against sentimental comedy, in the late-18th century, Goldsmith and Sheridan introduced the "new comedy of manners" that kept the benefit of moral behavior dramatized in sentimental comedy but returned otherwise to the shinning qualities of the 17th century comedy of manners while leaving the original objectionable immorality out of their revival.
Thus 17th century Restoration comedy of manners of Wycherley (The Country Wife) and Congreve is characterized by manners and conventions of high society, undisguised sexual dialogue, sexual temptation, denunciation of marital constancy, brilliant dialogue and witty (clever, quick thinking, satirical) characters, and satirical humor, while 18th century revival new comedy of manners of Goldsmith and Sheridan (School for Scandal, 1777) is characterized by by the same focus on manners and conventions of high society and the same kind of brilliant dialog and witty characters with continued focus on satirical humor but marriage has become important to uphold and morals are honored and lead to happy endings that are realistically worked out through well designed plots.
In other words, the new comedy of manners took a lesson in morality from the sentimental plays and applied it to the brilliance of Restoration comedy of manners to form a happy hybrid of brilliant satirical wit that held true to social values in morality.
[The Beggar's Opera (1728), John Gay, is an opera, thus not technically a drama/comedy, written during the sentimentalist period following after the Restoration comedy of manners period beginning with the end of Cromwell (1660) and ending c. 1688-1698, with the first sentimental comedies occurring c. 1696-1701 (the first anti-sentimentalist "new comedy of manners" play, Goldsmith's Good-Natur'd Man, appeared in 1768).]