While most puffballs are not poisonous, and the poisonous puffballs are typically quite distinct from the non-poisonous ones, puffballs often look similar to young agarics, especially the deadly Amanita family. It is for this reason that all puffballs gathered in mushroom hunting should be cut in half. Puffballs have an internal 'cup' shape, not a 'T' shape.
Major orders:
Lycoperdales, Tulostomatales, Nidulariales (related to Agaricales),
Geastrales and Phallales (related to Cantharellales),
Sclerodermatales (related to Boletales)
and various false-truffles (hypogaeic gasteromycetes) related to different hymenomycete orders.
Similarly, the true truffles (Tuberales) are gasteroid Ascomycota. Their ascocarps are tuberothecia.