What is exact way to do k-fold validation? What is exact way to do k-fold cross validation?  
A) Way 1 :
1. Split data into train set, test set
2. Apply k-fold validation on train set
3. Find best estimator from average of each validation score
3. Calculate final score on test set with best estimator  

B) Way 2
1. Apply k-fold validation on entire data
2. Calculate average of each validation score
3. Using it as a final score

So far I have known that Way 1 is exact way. I'm confused there many articles using the term 'test set/split/fold' instead of 'validation set/split/fold'. And they are using the average score on each validation score as final score.  
What is exact way?
 A: Both ways can be correct (or not) depending on what the purpose of the procedure is. 


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*A) uses cross validation for optimizing some hyperparameters (e.g. model complexity) and then tests the optimized model with the "test" data. (This latter step can be done by an outer, separate cross validation: see double or nested cross validation)

*B) uses cross validation for validation (or rather, verification). I.e., to estimate generalization error.
The term "cross validation" refers only to this particular scheme of splitting data (drawing without replacement and calculating a pre-determined number of surrogate models so that each case is used for testing exactly once). It can be embedded into larger procedures, such as in A).
Optimization and verification (validation) are two totally different tasks. The connection is that optimization can use verification results. 
As you say,  there's unfortunately a rather confusing 2nd "connection": the term "validation". Validation in my field (analytical chemistry/chemometrics) means that you make sure your method is fit for purpose (i.e. solves the task at hand) and a subset of this is verification which means showing your method (model) meets its specfications. The "validation" in cross validation refers to this: cross validation is a method to estimate model generalization errors.
The confusion arises because in the "train-validation-test" splitting terminology, it is actuatlly the "test" set that is used for verification/validation whereas the so-called "validation" set is used for optimization instead.
(Personally, I decided to try avoiding this confusion by using the terms optimization or auto-tuning and verification, respectively)
Summary: currently, there's no other way than understanding from the paper text what exactly is done to find out whether the approach is valid or not. 
