Is it possible to have same result for knn classifier and kmeans? Could we achieve similar grouping or results for a set of data, if applied with either Knn and k-means
 A: It's not sufficient that the $k$-NN and $k$-means both find  strong  signals.
Let us  imagine  data on a large number of cats and dogs owned by single-person households.  We could measure many variables on the pets --  size,  appearance, genetics -- and we  would expect $k$-means to  give a very clear 2-cluster solution  with dogs in one cluster and cats in the other.
But we were actually interested  in differences between pets owned by men and women. You could imagine (or at least I could)  that $k$-NN could do pretty well at predicting the gender of owners from information about the pet, but that the  $k$-NN classification would cut across the original $k$-means clusters.
A: Technically, you could achieve exactly same result by coin tossing as with classification algorithm, it would be hardly unlikely, though possible. More seriously, $k$-means is a clustering algorithm, so unsupervised learning, while $k$-NN is a classification, so supervised algorithm. Unless the labels in your data are about something unrelated to rest of the data, you could expect that there are some similarities between samples with same labels, hence that clustering algorithm can, but does not have to, group those observations together in a cluster, or clusters. However since $k$-means does absolutely nothing to match the labels, you do not have any guarantees that it will find clusters related to the labels.
