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This is more understandable than the Wikipedia entry.


Mathematical modeling is the process of creating a
mathematical representation of some phenomenon in
order to gain a better understanding of that
phenomenon. It is a process that attempts to match
observation with symbolic statement. During the
process of building a mathematical model, the modeler
will decide what factors are relevant to the problem
and what factors can be de-emphasized. Once a model
has been developed and used to answer questions, it
should be critically examined and often modified to
obtain a more accurate reflection of the observed
reality of that phenomenon. In this way, mathematical
modeling is an evolving process; as new insight is
gained, the process begins again as additional factors
are considered. “Generally the success of a model
depends on how easily it can be used and how accurate are its predictions.” (Edwards & Hamson, 1994,p.3)

What is the difference between the two?

Another explanation from Britannica.