Akatsuki (暁; Literally meaning "Dawn" or "Daybreak") is a criminal organization of S-Class missing-nins and is the most wanted group in all of shinobi world. Their main goal is to collect all of the Tailed Beasts for their plan of world domination. As such, Akatsuki, despite initially having a minor role during Part I, have become the primary antagonists in Part II.
--taken from Naruto.Wikia.org
It doesnt matter if Zabuza wasn't as strong as the Seven Swordsmen, he was labeled S-Class in the MANGA canon. Which is something Hokages typhically deal with. Not only that, but as a boy before he even qualified to become a ninja, he butchered the years graduating class. Kakashi became a Chunin at age 6. He hasn't been in the hospital for MONTHS after using his powerful techniques. Normally they are a few days of rest. If Tsunade has enough time to make others do her work, drink sake with Jiraiya, and drink tea while Jiraiya is fighting Pein, then he certainly has a few days to recover. S-Class is a STATUS of a person or a mission, and not a rank. Kage is a rank. S-Class ninja are feared. They also tend to have nicknames (Jiraiya the Toad Hermit, Tsunade the Slug Queen, Orochimaru the Giant Snake, Hiruzen Sarutobi the Professor, Kakashi the Copy Ninja, The Demon Zabuza, The Fourth Hokage "Konoha's Yellow Flash")
Also taken from naruto.wikia.org:
There are also S-Class missions, the highest paying and most dangerous type of mission a ninja can go on. These missions are exclusively assigned to highly skilled Jonin or large squads of ninja. S-Class is also a designation given to extremely powerful missing-nin, earning them a place in their village of origin's Bingo Book. Every member of Akatsuki is an S-Class criminal. Fans of the series will sometimes classify powerful ninja who are still loyal to their village as S-Class, such as the Sannin or other Kage-level characters, but this is arbitrary.
