[genericpseudo]

Close but not quite. The difference between (soft) SVM and a kernel linear classifier is choice of loss function; SVM minimizes hinge loss, linear regression minimizes squared loss.

(Choice of different loss functions will also give you Elastic Net, LASSO, logistic regression. From an engineering point of view I tend to think of the entire class as being different flavors of "stochastic gradient descent", in the spirit of Vowpal Wabbit etc.)