They starts from the same equation as below.
y = w*x + b
But they solve it differently. MLR specified the w and b by minimizing the square error whereas SVM specified w and b by minimizing the loss function defined by C and epsilon.
I am wondering if the result of regression is significantly different. I guess that if the given data set is clean and well-explained by input features, the resultant w and b between SVM and MLR will be close. Putting my original question differently, I don't find any reasons to use linear SVM regression over multiple linear regression.