What is the difference between SVC and SVM in scikit-learn?

Question

From the documentation scikit-learn implements SVC, NuSVC and LinearSVC which are classes capable of performing multi-class classification on a dataset. By the other hand I also

Answer 1

They are just different implementations of the same algorithm. The SVM module (SVC, NuSVC, etc) is a wrapper around the libsvm library and supports different kernels while LinearSVC is based on liblinear and only supports a linear kernel. So:

SVC(kernel = 'linear')

is in theory "equivalent" to:

LinearSVC()

Because the implementations are different in practice you will get different results, the most important ones being that LinearSVC only supports a linear kernel, is faster and can scale a lot better.