Optimal separating hyperplanes and relaxations ✔ SVMs: nonlinear generalizations of separating hyperplanes ✔ SVM as a function estimation problem ✔ Kernel logistic regression ✔ Reproducing kernel Hilbert spaces ✔ Connections between SVM, KLR and Boosting.
I assume that you mean a "support vector machine" (SVM)?
Essentially an SVM is designed to create a more complex decision boundary than is the case with the logistic function. One version using a simple linear kernel function (LS-SVM) would I guess be broadly equivalent to the linear boundary condition of a typical logistic model. However, in many cases you would specify a more complex function (e.g. RBF) when looking at classification models using SVMs.
I suggest that you read 'cross validated' on Stack Exchange for more discussion of these issues - e.g.
https://stats.stackexchange.com/questions/95340/comparing-svm-and-logistic-regression
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