Sometimes a media report on Westminster will mention reports "by MPs", or by "committees of MPs". Such phrases don't highlight the nature of the group involved.
Select Committees are set up by the House of Commons. (There are also Select Committees in the House of Lords and Joint Committees). The most well known are the Departmental Select Committees, which are covered by Standing Order 152. Further related Standing Orders are 121-152K (2015 Standing Orders as amended by the Addendum of June 2015). One of the most well known, and influential select committees is the Public Accounts Committee - which I attended on Tuesday.
There is a video on committees - accessible here.
APPGs (All Party Parliamentary Groups) are set up by MPs and Peers themselves. They are wholly unofficial. They can range from APPGs promoting serious policy issues, to ones celebrating a particular leisure or cultural interest of its members (such as the Jazz Appreciation APPG). A register of APPGs is regularly published (the latest - March 2015 - is available here)
The range can be seen from the last 20 entries -
West Coast Main LineWest Midlands
Wine and Spirit
Women and Enterprise
Women in Parliament
Women in the Penal System
Women, Peace and SecurityWomen’s Sport and Fitness
Wood Panel Industry
Yorkshire and Northern Lincolnshire
Young Disabled People
Zoos and Aquariums
A guide to the rules governing APPGs can be found here.