When calculating loss we consider only a single data point, then we use the term loss function.
Whereas, when calculating the sum of error for multiple data then we use the cost function. There is no major difference.
In other words, the loss function is to capture the difference between the actual and predicted values for a single record whereas cost functions aggregate the difference for the entire training dataset.
The Most commonly used loss functions are Mean-squared error and Hinge loss.
Mean-Squared Error(MSE): In simple words, we can say how our model predicted values against the actual values.
MSE = √(predicted value - actual value)2
Hinge loss: It is used to train the machine learning classifier, which is
L(y) = max(0,1- yy)
Where y = -1 or 1 indicating two classes and y represents the output form of the classifier. The most common cost function represents the total cost as the sum of the fixed costs and the variable costs in the equation y = mx + b