As noted by Bitwise in their answer, k-means is a clustering algorithm. If it comes to k-nearest neighbours (k-NN) the terminology is a bit fuzzy:

• in the context of classification, it is a classification algorithm, as also noted in the aforementioned answer

• in general it is a problem, for which various solutions (algorithms) exist

So in the first context, saying "k-NN classifier" can actually mean various underlying concrete algorithms that solve the k-NN problem, and their result is interpreted for the classification purpose.

These are two different things but you might find it interesting that k-means algorithm is one of various possible methods for solving the k-NN problem (Marius Muja and David G. Lowe, "Fast Approximate Nearest Neighbors with Automatic Algorithm Configuration", in International Conference on Computer Vision Theory and Applications (VISAPP'09), 2009 PDF)

As noted by Bitwise in their answer, k-means is a clustering algorithm. If it comes to k-nearest neighbours (k-NN) the terminology is a bit fuzzy:

• in the context of classification, it is a classification algorithm, as also noted in the aforementioned answer

• in general it is a problem, for which various solutions (algorithms) exist

So in the first context, saying "k-NN classifier" can actually mean various underlying concrete algorithms that solve the k-NN problem, and their result is interpreted for the classification purpose.

These are two different things but you might find it interesting that k-means algorithm is one of various possible methods for solving the k-NN problem (Marius Muja and David G. Lowe, "Fast Approximate Nearest Neighbors with Automatic Algorithm Configuration", in International Conference on Computer Vision Theory and Applications (VISAPP'09), 2009 PDF)