I know that you can drill down on the particular language or country version of google from "Search tools," but even discounting for that, and removing personalisation etc, I'm still seeing different results for the same search between google.com and google.co.uk, for example. All things being equal, are these really supposed to be showing exactly the same results?
are these really supposed to be showing exactly the same results?
No. There might be a lot of overlap, but
google.com targets its results to a US audience and
google.co.uk delivers results that are supposed to be more relevant to a UK audience.
The results returned aren't necessarily "local" to each region, however, they are deemed to be relevant to someone in that region when searching for whatever phrase they have searched for.