Primary root: the first root to emerge from a germinating seed (starts as the radicle). Since the primary root is present within the embryo, this class of root is embryonic.
Lateral roots: roots that form from other roots. The lateral roots that form from the primary root are first order lateral roots; the lateral roots that form from the first order laterals are second order laterals and so on. This class of root is post-embryonic.
Seminal roots: form adjacent to the radicle and dominate the early root growth in monocots. This root type is embryonic.
Adventitious roots: any root that forms from anything other than another root. This includes roots that form on the base of stem cuttings, from leaf explants, from stems in flooded plants and also from nodes of cereal crops (often called crown roots). These root types are very diverse (Steffens and Rasmussen, 2015) so can include both embryonic and post-embryonic roots.