【Affair】 , 【business】 , 【concern】 , 【matter】 and 【thing】 come into comparison only when they are little more than vague or general terms meaning something done or dealt with.

Some or rarely all are used interchangeably in certain similar collocations such as his own 【affair】 , 【business】 , 【concern】 ; public and private affairs, concerns, matters, 【business】 ; a sorry 【affair】 , 【business】 , 【matter】 , 【thing】 ; affairs, matters, things are in good condition. However, a degree of precision is possible, for each word carries distinctive implications which are not always obscured.

【Affair】 suggests action or performance; it may imply a process, an operation, a proceeding, an undertaking, a transaction.

• seeing a book through the press is a laborious and time-wasting 【affair】
  —T. H. Huxley

In the plural it often denotes transactions of great importance such as those involved in the management of finances or in the carrying on of diplomatic negotiations.

• men of affairs
• he had married a rich woman and administered her affairs. He was not supposed . . . to have any affairs of his own
  —Mary Austin

【Business】 usually stresses duty or office; sometimes it suggests an imposed task.

• because a 【Thing】 is every Body’s 【Business】 , it is no Body’s 【Business】
  —Steele
• the flight of his imagination is very swift: the following of it often a breathless 【business】
  —Day Lewis

【Concern】 suggests personal or direct relationship: it often implies an important bearing on one’s welfare, success, or interests; thus, something is not one’s 【concern】 because it has no bearing on one’s interests, welfare, or success.

• the simplest way out of the difficulty was to do nothing and dismiss the 【matter】 as no 【concern】 of theirs
  —Conrad

Sometimes 【concern】 is preferred to 【affair】 when that which requires attention involves a degree of anxiety or solicitude.

• the concerns of state

【Matter】 usually is more objective as well as more vague than the preceding words. It generally refers to something that is merely an object of consideration or that is to be dealt with <he will attend to these matters very soon.

• this is still one 【matter】 in dispute
• never insist without carrying the 【matter】 through
  —Russell

【Thing】 is even more indefinite than 【matter】 and is often intentionally used when there is a desire to be vague or inexplicit.

• he promised that things would be better in the future
• first things should come first
• more things are wrought by prayer than this world dreams of
  —Tennyson
• these things are managed so well in France
  —Harte