The difference between linear and curvilinear correlation is set up on the principle of the ratio of change between the variables. The difference between these two depends on how they appear in a scatter diagram.
Meaning of Linear Correlation
When a ratio of change is constant the correlation is supposed to be linear. Further, when the total amount of product in a warehouse is increased by increasing the number of operators, is one of the examples of linear correlation. In another term, when the entire points on the scatter diagram start to bend close to a line which is similar to a straight line, then the correlation is assumed to be linear.
Meaning of Curvilinear Correlation
When a ratio of change is not constant the correlation is supposed to be linear. In another term, when the entire points on the scatter diagram start to bend close to a smooth curve, then the correlation is nonlinear (curvilinear).
Linear and Curvilinear Correlation
Positive Correlation  Negative Correlation 
Two variables are said to have a positive correlation when they move in the same direction i.e. change occurs in them in the same direction.
i.e. â€˜Xâ€™ â€˜Yâ€™ and â€˜Xâ€™ â€˜Yâ€™ Example,

Two variables are said to have a negative correlation when they move in the opposite direction i.e. change occurs in them in the opposite direction.
i.e. â€˜Xâ€™ â€˜Yâ€™ and â€˜Xâ€™ â€˜Yâ€™ Example,

Linear Correlation  Curvilinear Correlation 
There exists a linear correlation if the ratio of change in the two variables is constant.

There exists a curvilinear correlation if the change in the variables is not constant.

Simple, Partial & Multiple Correlation 
Simple Correlation â€“ When we consider only two variables and check the correlation between them it is said Simple Correlation. For example, radius and circumference of a circle.
Multiple Correlation â€“ When we consider three or more variables for correlation, it is termed as Multiple Correlation. For example, Price of Cola Drink, Temperature, Income and Demand for Cola. Partial Correlation â€“ When one or more variables are kept constant and the relationship is studied between others, it is termed as Partial Correlation. For example, If we keep Price of Cola constant and check the correlation between Temperature and Demand for Cola, it is termed as Partial Correlation. 
The above mentioned is the concept, that is elucidated in detail about the â€˜difference between linear and curvilinear correlationâ€™ for the class 11 Commerce students. To know more, stay tuned to BYJUâ€™S.