I can answer for the UK. You can use this formula...
Tourist Visa = Visitor Visa = Family Visitor = Entry Clearance
'Entry clearance' is the 'official' terminology and all of UKVI's internal documentation uses that term. "Entry Clearance" is preferred because it tells everyone that the visa was issued by an overseas post. When an American (Canadian, etc) applies for leave to enter at a port, the 'official' term for the stamp in their passport is "Entry Certificate" (whether it constitutes a 'visa' or not is a matter of context). The definitions are given in the Immigration Act 1971 and have not changed since then.
When a person is actually in the UK on one of those, their legal status is "Visitor"; there is no such legal status as "Tourist". A person is either a visitor with an entry clearance or a visitor with an entry certificate.
Entry clearance takes the form of a visa (for visa nationals) or an
entry certificate (for non visa nationals). These documents are to be
taken as evidence of the holder's eligibility for entry into the
United Kingdom, and accordingly accepted as "entry clearances" within
the meaning of the Immigration Act 1971.
Source: Paragraph 25
"Family Visit Visa" and "Business Visit Visa" were abolished last spring. People still use the terms to describe the premise of their visit, but everybody gets a "Standard Visitor Visa".
It was only recently that they decided to use the term 'visa' in the laws; before that, the term 'entry clearance' or 'entry certificate' or 'leave to enter' was used. The change of language is part of UKVI's ongoing initiative to become more customer focused and professional.
For the part of your question about what's preferred... 'entry clearance' is preferred when it describes something an overseas post issued, and hence the most precise. Secondarily, "Standard Visitor Visa" usually describes the same thing. And 'visa' is preferred for everything else (including 'entry certificates').
A note on Schengen: Schengen uses a number of the same concepts, but the terminology was never imported.
A final note on terminology: Americans (Canadians, etc) may use the term "I came over on my passport". In the context of UK law, it means they applied for leave to enter at a port and received an entry certificate.
This whole answer is bounded by the domain of 'visitors'. Spouses get entry clearances as do workers as do performers and so on, but these sorts of visas are out of scope here.