Almost all the wood in trade that is labeled poplar is Tulip Poplar (Liriodendron tulipfer), as you say. Great wood when properly dried, for painted furniture or woodwork - stable and easy to machine. True Populus spp. in North America are the various Cottonwood and Aspen species. The Aspens can be decent lumber - kind of a poor man's birch - but they don't grow all that big and most of what is harvested ends up as pulpwood or veneer. Cottonwood on the other hand, particularly the Eastern Cottonwood (P. deltoides) grows very quickly and gets huge - a 50 year old tree can easily be 3' or more in diameter at breast height, and a 100 year old tree (which is about the limit of their life span) the most massive trees you'll find in the Midwest. They'll also grow almost anywhere, from sand to heavy clay. But the wood is awful stuff to try do anything with - it corkscrews right off the saw as often as not, and only gets worse in drying. And the wood is light and coarse, and not strong. It goes into pallets and wood stoves around here at least.