Let's say we have trained a Support Vector Machine with a Gaussian Kernel. When we feed our model an example, it classifies it based on its similarity to landmarks (distance to examples in our training set).
If instead our model is a K-Nearest Neighbors algorithm, with k=size of the training set, it classifies a given example based on its distance to examples in our training set (similarity to landmarks).
I know the math behind SVM and KNN is different, but on a high level, are they both employing the same idea? What am I missing if I think they are doing the same thing in different ways?