The part you're missing is the only thing they had in common was playing music on a turntable outside.Now here is the difference and why HipHop is closer to Disco.
because he along with the other HipHop dj's was actually adapting American Funk/Disco music along with Disco dj'ing techniques. Disco djing is totally different from the Jamaican sound system style. For example
I don't how anyone could look at the sound system turntable operators and think HipHop djing came from that considering they didn't even use 2 turntables and a mixer for continuous mixing. That came straight from Disco.
Herc tried to the Disco Djing style but he never caught on. Disco djing is where Herc got the idea to use 2 copies of the same record with 2 turntables. They never did that in Jamaican sound system culture. For example
This video is a good example of the transition from pure Disco Djing to HipHop djing before the scratching and other tricks came in. This is like playing the break parts but with smooth disco djing skills.
This is a great example when it fully came into it's own and added new ideas such as back spinning and scratching
You will not find anything like this in the Jamaican Sound system operators because it relates more to Disco
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Jamaican toasters didn't rap at all as I've pointed out millions of times. We have tons of examples of the Jamaican toasting style and it's nothing like rapping
A bit more on the differences between the Disco Dj's and the Herc scenes and how they impacted the formation of HipHop
From the article below:
"In contrast to Herc's pulled-ups and needle drops,
disco dj's favored smooth segues from track to track. They also tended to rap in a more mellifluous style, relating directly, if casually, to the steady beats of the music they were playing, and stringing together long verse like presentations of their own set of stock phrases rather than the freer, more fragmented interjections of the Herculords and their streetwise colleagues. The next generation of hiphop Dj's and Mc's would synthesize these distinct strands, refining (if not outright commercializing) "street" style while bringing in a harder edge to the smooth surfaces of club rap and disco djing."
It didn't....dancehall and rap are cousins through older American roots. If anything HipHop influenced what became modern dancehall. As I once said...
early jamaican toasting style
Supercat basically hints at it here