Meaning of Linear Correlation
Linear correlation is referred to as the measure of relationship between two random variables with value ranging from 1 and 1. It is proportional to the covariance and can be interpreted in the same way as covariance.
Linear correlation is also said to be based on a straight line relationship between two random variables.
Meaning of Curvilinear Correlation
Nonlinear or Curvilinear correlation is said to occur when the ratio of change between two variables is not constant. It can happen that as the value of one variable increases, similarly the value of another variable increases. This will happen till a certain point, after which the increase in value of one variable will result in decrease in value of the other variable.
The graphical representation of a curvilinear correlation is said to be like an inverted U.
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.
I have understood the difference, thanks