A model according to Princeton dictionary is "the act of representing something (usually on a smaller scale)" 

For example 
* a model car is just a representation of a real car - but the model car is not actually a real street car  ''JustIsaDangerousWord.''
* the relational model does not equal a relational database implementation - but rather a model of ''relational'' structure.

Interestingly enough - one could tweak a model car to actually drive by putting electronic motors in it and an ant or an insect - and it would no longer be a model in some senses (although it is still not a full street car, it could even be placed on the street, although it may get squashed quickly). That, however, is when we are dealing with a physical model car.

Maybe we need to clearly separate '''thinking models''' from '''physical models'''. Physical models do exist.

Maybe the term ''model'' is too overloaded and/or too vague.

''IIRC, there are already rigorous mathematics and scientific definitions for models, theories, axioms, and the relationships between these.  Going to the layman's dictionary won't be of much help if you wish to understand the use of the word 'model' in 'RelationalModel'.''

The relational model is a theoretical model ('''representation'''). Like a model car, it is ''just a representation''.  Defining phrases in '''clear concise''' English is fairly helpful, despite your problems with the act (more like your disease - you seem to be a verbose BuzzWord addict who uses DoubleSpeak a lot yourself - and I can find at least 3 people who'd agree).  

* [Huh?  Whatever his failings may be, using BuzzWord''''''s and DoubleSpeak isn't among them.  You seem to be confusing "buzzwords" with "terminology", and "doublespeak" with "rigour".  His verbosity -- and indeed his suggestion above -- appears to be an attempt to ''avoid'' using buzzwords and doublespeak, in fact.]

You'd be surprised that the history of the phrase ''relational'' and ''foreign key'' which Codd coined, did not involve some rigorous mathematical decision. Codd came up with the term relational and foreign key while half jokingly listening to the President on the radio (or some similar situation). The speaker was talking about ''foreign relations'' with other countries, AFAIR. Codd jumped on this and decided to simply use what he heard on the radio one day. Take note: people coin phrases for fun, sometimes - even while listening to radios or while creatively munging together interesting words that didn't originally apply to the topic.

Please don't over-analyze so much - and do consider the extremely helpful concise meanings in your dictionary. Do also consider actual history and actual meanings, rather than dressing definitions up with icing sugar. I've always considered this wiki slightly an AntiPattern: people over analyze definitions and fill pages with needless BuzzwordBingo - when in fact usually there is a clear and concise meaning and history laying underneath any term or pattern.   Similarly, when I looked into Monads I went straight to the horses mouth (the inventor) to find out about the actual history and meaning behind Monads and Haskell - because people who I'd listened to on this wiki, didn't have the skill or capability of speaking in a clear and concise manner about the topic.

Do consider taking such a path to research, please, instead of filling pages with so much assumptive DoubleSpeak and cake icing.