Don't compare The All-mighty Zeppelin to common heavy metal.
Zeppelin is heavy at times, and Sabbath is heavy all the time, but they are by no means metal(neither is Queen). The first true heavy metal band was Judas Priest.
1980 was when the Albums British Steel by Priest, and Iron Maiden by Iron Maiden came out.
These albums shaped the metal scene of the 80s and directly influenced other great ablums like Kill 'em all (Metallica) and Reign in Blood (Slayer).
Zeppelin did influence These bands, but they also influenced many progressive rock acts such as Pink Floyd, Genesis and Yes. At the height of the popularity of progressive rock, many musicians and listeners were fed up with the 20 minutes solos performed by Pete Townsend and the like. Thus was formed the Genre Punk. Early Punk included acts like Iggy and the Stooges and a few years later The Ramones. They were influenced by Led Zeps heavy, fast, and sometimes mindless songs (such and Rock 'n Roll and Immigrant Song). After a Ramones concert in London 1976, 3 of the most important punk bands were formed, these were: Sex Pistols, The Clash and Generation X. All of these bands from punk and prog rock influenced heavy metal in the 80s.
Another important band to note is the British rock band Motorhead. These guys are frequently referred to as being "Heavy Metal", while their influence on the genre is unquestionable, the frontman Lemmy has said in an interview that he more closely associates his band with punk rock, rather than heavy metal (he also admitted in another interview that he tried to teach Sid Vicious from the Sex Pistols how to play bass, emphasis on the tried).
Heavy Metal was a culmination of the best parts of progressive rock and punk rock. These genres were influence by Led Zeppelin and again came full circle to create heavy metal.
Led Zeppelin is a rock and roll band.