What are the differences between SVC, NuSVC, and LinearSVC?
In scikit SVC and nuSVC are mathematically equivalent with both methods based on the library libsvm. The main difference is that SVC uses the parameter C while nuSVC uses the parameter nu.

LinearSVC is based on the library liblinear. As the documentation says, LinearSVC is similar to SVC with parameter kernel='linear', but liblinear offers more penalties and loss functions in order to scale better with large numbers of samples. Please check out this question and this question for more details.