You'll find similarities to the original manga across EVERYTHING in GITS. The original movie was a rehash on certain chapters of the original manga. Innocence is an expansion upon another different chapter from the original manga while throwing in a few references to Man-Machine Interface.
Stand Alone Complex recreates and references many scenes across the entire manga series at some point or another, but Solid State Society mainly references Human-Error Processor the most.
So with that in mind, since the original movie referenced the manga, and you're finding similarities between the original movie and SSS, it's because both are referencing the manga.
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"A SMARTER hitman would have shot first..." - Major Motoko Kusanagi