The three categories differ in transmission and legal-epistemic effect:
Mutawatir: widespread independent transmission; certainty.
Mashhur: initially ahad, then widely received; settled reassurance.
Ahad: below the threshold of mashhur; may require practice if qualified, without yielding the certainty of tawatur.
The textbook’s illustrations are the Qur’an for tawatur and reports about wiping over khuffayn for mashhur. Many other hadith reports are within the ahad category.
The distinction is not that every ahad report is rejected. Its admissibility and use depend on recognized conditions.