Upvote:2
The sentence is a little unclear but the first criterion is indeed your citizenship, and many Italian residents do need a visa/entry clearance to visit the UK. Outside of some special cases (members of the family of an EU citizen mainly), you can use the regular widget.
In this case, Moldovan citizens do need a visa even if they are Italian residents.
Upvote:5
I agree that the site is slightly out of whack in the way you have pointed out. The text...
Check if you need this visa if youβre visiting from outside the European Economic Area (EEA) or Switzerland.
...should say...
Check if you need this visa if your passport or travel document is from outside the European Economic Area (EEA) or Switzerland.
The travel document in this context does not mean residence permit, but the document a person presents to gain entry to a country. About 99% of the time it is a passport, but sometimes for example it is a special card issued by the United Nations and sometimes a refugee identification card. That's why they have to say 'travel document' instead of just 'passport'.
For your specific case, it's about a Moldovan who has regularised in Italy. The UK doesn't care about that. Moldovan nationals need to have an entry clearance before they arrive, and the entry clearance needs to go into their passport. They should apply online by following the links you gave.
That, presumably, answers your main question. For the part of your question about the UKVI site being inconsistent, you will find a link at the bottom of most pages entitled "Is there anything wrong with this page?". You can use it to describe the problem you found. You will get back a boiler-plate email explaining that they cannot help you get a visa and you should see a lawyer. Admittedly, it has nothing to do with problems on their site, but unfortunately that's the way the web site works at UKVI.