Are you talking about Yellowstone or New Madrid?
Yellowstone.
New Madrid is defined by a failed rift arm underlying (and forming) the Mississippi Valley. There's a Precambrian Mid-Continent failed rift in the same general area as the Mississippi Valley, but the failed rift we're talking about is associated with the Jurassic opening of the Gulf of Mexico, which actually began in the Triassic, about the same time as the Atlantic rift zone.
The geology of rifting is that the rift usually forms as a three-armed rifting area, generally star-shaped, over a spreading center that underlies a craton. As the rift develops, two of the arms open wider than the third; the two wider arms become the new rift and spreading center => ocean basin, and the third arm stops spreading and becomes quiescent, with residual geological activity (volcanism, heat flow, subsidence and seismicity). Hence the New Madrid Zone.
Yellowstone is a hot spot, a mantle plume that blowtorches the crust plates above it with very high heat flow. Right now it's melting its way repetitively through the two overlapping plates under western North America (the leading edge of the overridden Pacific and Nazca Plates roughly defined by the Front Range of the Rockies). Hot spots are largely independent of spreading centers. The Hawaiian Island chain (which includes French Frigate Shoals, the Farallones, and Midway) is another hot spot.