A puncture is a hole made on the surface of the paper. It is a dot, a point, or node. In TMS punctures tell you what note to play.
A thread is simply a line segment made when sewing (or drawing). It connects two punctures. A thread in TMS shows you where to go and what note to play next.
A seed is the fundamental building block of Tahigami. It is a triangle and has 3 punctures and 3 threads.
Two contiguous seeds share a common thread. They form a bud. And, as in a flower, a bud has potential to bloom. A bud has 5 threads and 4 punctures.
A blossom is a fully-formed Tahigami element. It has multiple seeds, threads, and punctures. A Blossom in TMS generates melodies.