There are literally dozens of different varieties of hops, in much the same way there are dozens of different breeds of dogs. Just as a Chihuaua and a Great Dane are both Canis Lupus, a Galena Hop and a Goldings Hop are bot Humulus Lupulus, separated by vastly different lineages and genetics. New hop varieties are often developed by selective crossbreeding of existing variants, to generate different flavor profiles by adjusting the acidity and oil content of the hop.
Like different breeds of dogs, different hop varieties are often the products of hundreds of years of genetic development in a particular climate - the Pacific Northwest, especially the Yakima Valley and Cascade Mountains in Washington, Oregon and Idaho, is known for it's production of very strong, highly acidic hops that impart a very strong bitter flavor - take a sip of a Sierra Nevada IPA and you'll instantly recognize that classic blend of the 'three C's'.
By contrast, traditional hops grown in England and on the European continent tend to be more mellow and aromatic - especially the so called 'noble hops' popular in many less bitter tasting German and Czech beers. Still others, like Japans Sorachi Ace, offer a more citrus bite to the beer they're added to. While these differences are not directly a product of climate, it's doubtless true that climate has had an impact on the development of variation amongst the various hop lines that have been bred through the centuries - and especially over the past 50 years or so.
Put another way: New World vs. Old World Hops is a meaningful distinction, but it has less to do with climate and more to do with the difference in cultivation practices and the specific varietals popular with farmers in various regions. Growing conditions may have some impact, but the specific lineage matters much, much more. The fact that those lineages tend to have significant geographic commonalities is as much an accident of history as it is of varying conditions, but it's nonetheless sufficiently meaningful that, in particular referring to hops from the Pacific Northwest evokes a very specific and comprehensible flavor profile in most educated beer drinkers.