What is the difference between the terms ‘Error’ and ‘Residual’? Sometimes these are used interchangeably, does it mean that they both have the same meaning?
Error vs Residual
Hi, According to me
Residual is the deviation of the observed data point from the best fit model.
Where as, Error is the difference between the observed value and the predicted value
We can say it as
residual analysis is done on train data.
error is calculated on test data.
In training data , we get difference between observed value and true value > Error
In test data , we get difference between estimated value and observed value > Residual

Residual :
First thing is Residual.
Residual(ei) means the difference between the actual(yi) observed value and the value that is predicted ( ie. ˆyi) by model.
ei = yi−ˆyi 
Error:
We have 2 types of errors:
i) Irreducible error: This error is not our hands like that might depend on that climate or that day patient activeness. We have no control on this.
ii) Reducible error: This error is caused by the predicted function is deviated from the actual function.
Out analytics, the goal to reduce this error always.
Usually, we have train error ( Error occurred on the train data ) and test error (( Error occurred on the test data ).
But our goal is to minimize the test error. Test error can be reduced by minimizing the Residual error.
I hope it helps.
Error is a mistake done by human (data entered wrong by someone).
Residual is an odd object from natural behavior(data is calculated normally).