Difference between RFE and SelectFromModel in Scikit-Learn
They effectively try to achieve the same result but the methodology used by each technique varies a little. 

RFE removes least significant features over iterations. So basically it first removes a few features which are not important and then fits and removes again and fits. It repeats this iteration until it reaches a suitable number of features. 

SelectFromModel is a little less robust as it just removes less important features based on a threshold given as a parameter. There is no iteration involved.