The doughnut is formed by concentric alternating echogenic and hypoechogenic bands. The echogenic bands are formed by mucosa and muscularis whereas the submucosa is responsible for the hypoechoic bands.
The crescent is formed by mesentery which is dragged into the intussusception. It is naturally located only on one side of the bowel and therefore forms a crescent which is echogenic.
It is thus the transverse equivalent of the pseudokidney sign.