Jack, turf is a great big subject, and like TEPaul says, there is room in it for everyone...
There are several ways to characterise growth habits of turf. First, warm season and cool season grasses. i.e. bermuda's VS bentgrasses, fescues, blues, and the transitional Zoyzias.
But, more in line with your question is growth habits in leaf blades and rooting. There are those that are stoleniferous, or rizomatic (meaning heavy rooting and tiller spreading anatomy where growth of leafs keep cropping up out of spreading tillers) and bunch like, meaning rooting that goes straight down off of one main root and grows the leafs in small bunches straight up (more or less) Then there is the leaf textures, which can range from fine to coarse with upright to laid down habits. Obviously, that all effects the how the ball sets up upon or among those turf leafs blades and is effected by the height of the cut of those leafs. The really agressive rizome and stolen growth turf must be core aerated and sliced in some fashion or they become a thatch fest of puffiness.
A good book for the basics is James Beard's, "Turf Management for Golf Courses".