Audax

Audax is the name given to long distance cycling, run under rules set by Audax UK. Audax UK has a useful set of FAQs, from which the following description comes:

They are NOT races. People ride them more in the spirit of an event like the London Marathon, everyone riding to their own limitations with the primary objective to just 'get round'. These events suit everyone, clubmen, time-trialists, recreational riders, cycletourists, 'born again' cyclists, young and old, male and female. And you'll see all sorts of machines - bikes, tandems, trikes, recumbents, and occasionally even stranger things ...
Size of entry varies greatly but is typically around 100 starters. Small local events may have just a handful of riders while a few popular events attract 200 starters or more.
The routes typically feature a few fast main roads and a lot of quiet, scenic lanes. Many events are quite hilly, some are extremely hilly, and even the flatter ones usually have one or two challenging climbs. Some events are noted for the quality of home-cooked food and tender loving care supplied along the way. But most are not - self-sufficiency is a highly-regarded quality in AUK.
On the same theme, 'support' - for example a following car - is very much frowned upon. There are maximum and minimum time limits, which are designed to suit everyone from the fittest of recreational riders, to more occasional riders who have plenty of determination. Each rider carries a 'brevet card' which is stamped at intermediate checkpoints and at the finish, and which is later returned to the rider as a certificate of their achievement.
The success rate on these events is very high - probably only about 10% fail to finish.

Our club' most notable Audaxer is Steve Abraham, who's completed some astonishing rides (and along the way has competed in several 24h time trials). Through 2015 (and into 2016 due to an unfortunate accident), Steve has been trying to break a long-standing annual mileage record.

Some useful web links about Audax cycling

Taking part in an Audax ride

Audax UK FAQs

Sportives

Sportives are a more recent appearance on the cycling scene. Often seen as a race by the public, essentially these are fast social rides in which some pretty fast performances can be seen. Sportives are often presented as a 'challenge', generally relating to the amount of climbing the riders will do.

British Cycling has a web page about Sportives, including notes on what to expect and how to prepare for them. Here is a searchable events calendar. Riders can travel some distances for the more popular or challenging sportives, and NBRC supports the local Sportive, the Brickhill Challenge.