The green tracks (TABS, TABM, TABD) are the beta-advection models. They use the mean flow of the GFS winds over different layers with a correction made for the beta drift. The different variations loop in different ways depending on how deep of steering flow you want to consider. S is for shallow, M is medium, and D is for deep. They loop largely because the GFS shows a breakdown of the steering flow. It's my understanding that a skilled forecaster can make some interesting inferences about the cyclone environment based on the TABx tracks. As a general rule you'll probably want to ignore them and instead focus on TVCN (or maybe TVCX). It is the consensus of the best track models which as of 2018 are an equal weighting of GFS, ECMWF, UKMET, HWRF, and COAMPS.