Why does Local installation gets different results than https://nominatim.openstreetmap.org/search

I installed a local version of Nominatim on Ubuntu 22.04, using the instructions from here: Basic Installation - Nominatim 4.3.0 Manual
Downloaded and imported this database:
When searching for coordinates of an address, sometimes I get wrong results.
Trying to understand the reason, I ran the same query on Nominatim Demo - here, I got correct results.
I used the wikimedia data, as recommended.
Are the results supposed to be the same? What am I missing?

You will never get exactly the same results on a local installation as on nominatim.openstreetmap.org. The OSM data is from a different point in time and our servers usually run on bleeding-edge versions of the software, not on releases.

Right now, you will also get the PHP frontend when you follow the standard installation instructions, while nominatim.openstreetmap.org runs on the new Python frontend. You can try that out and see if results are better. Setup instructions for the frontend are in the Deployment section. Both frontends use exactly the same database, so you can safely switch back and forth without reimports.