m-w
Not rocket science, surely? 
 
 
Main Entry: 1ca·su·al 

 Function: 
adjective Etymology: Middle English, from Anglo-French & Late Latin; Anglo-French 
casuel, from Late Latin 
casualis, from Latin 
casus fall, chance — more at 
case Date: 14th century 1
: subject to, resulting from, or occurring by chance <a 
casual meeting>2 a
: occurring without regularity 
: occasional <
casual employment> b
: employed for irregular periods <a 
casual worker> c
: met with on occasion and known only superficially <a 
casual friend>3 a (1)
: feeling or showing little concern 
: nonchalant <a 
casual approach to cooking> (2)
: lacking a high degree of interest or devotion <
casual sports fans> <
casual readers> (3)
: done without serious intent or commitment <
casual sex> b (1)
: informal , 
natural <a 
casual conversation> (2)
: designed for informal use <
casual clothing> 
synonyms see 
accidental, 
random
 
Main Entry: 1for·mal 

 Function: 
adjective Etymology: Middle English, from Latin 
formalis, from 
forma Date: 14th century 1 a
: belonging to or constituting the form or essence of a thing <
formal cause> b
: relating to or involving the outward form, structure, relationships, or arrangement of elements rather than content <
formal logic> <a 
formal style of painting> <a 
formal approach to comparative linguistics>2 a
: following or according with established form, custom, or rule <lacked 
formal schooling> <a 
formal dinner party> <
formal attire> b
: done in due or lawful form <a 
formal contract> <received 
formal recognition>3 a
: characterized by punctilious respect for form 
: methodical <very 
formal in all his dealings> b
: rigidly ceremonious 
: prim4
: having the appearance without the substance <
formal Christians who go to church only at Easter> 
synonyms see 
ceremonial
 
Skimming these definitions makes me think that casual/formal is really a matter of attitude ... that Chanel can be worn in a casual, nonchalant way, and jeans & Keds can be worn in a formal way (a la ramrod).