How Linear SVM Regression and Multiple Linear Regression different in terms of the regression result?
They could potentially be very different, because linear regression penalizes using squared error while SVRs penalize absolute error. You might have learned that "outliers" can have an outsized influence on the regression line because of this--this won't be the case with SVR, however.

Furthermore, if the SVR you're talking about is like the one described here (great resource there, by the way) then choosing a larger $\epsilon$ will yield a flatter regression line/hyperplane, whereas you don't have such a tuning parameter for regular ol' linear regression. This parameter enables you to try to fight overfitting by flattening the regression line.