The Difference between Theoretical Modelling and Identification is given in the following table.
S.No.

Theoretical Modelling

Identification

1.

Model
structure follows from laws of nature. 
Model
structure must be assumed. 
2.

Modelling of
inputoutput behavior as well as the internal behaviour. 
Only the
inputoutput behaviour is identified. 
3.

Model
parameters are given as function of system properties. 
Model
parameters are numbers only. In general no functional dependency to system properties known. 
4.

Model is
valid for the entire class of processes of a certain type & for different operating conditions. 
Model is
valid for investigating system and within operating limits. 
5.

Model
coefficients are not known exactly. 
Model
coefficients are more precise for the given system within operating limits. 
6.

Models can
be built for nonexisting systems. 
Model can
only be identified for any existing systems. 
7.

The internal
behaviour of the system must be known and must be describable mathematically. 
Identification
methods are independent of the investigated systems and can be applied to many different systems. 
8.

Typically
lengthy processes which takes up much time. 
Fast process
if identification methods exist already. 
9.

Models may
be complex and detailed. 
Model size
can be adjusted according to the area of application. 
Excercise
Q1. Write down the differences between Theoretical Modelling and Identification.