> the common word you would use [for] PhD is professor or scientist
Those are not common words for people possessing a PhD, and that's good because they are totally inappropriate words.
A PhD is a type of qualification (a very unusual one, in that it requires original contribution to knowledge rather than just learning existing knowledge, but it's a qualification nonetheless). "Professor", in total contrast, is essentially a job title. It's very possible for someone to have a PhD and not be a professor. The most common case is where a PhD holder has simply not stayed in acamedia at all; actually this probably describes the vast majority of PhD holders (by simple maths of the number of PhD students per academic). Even for people in academia there is typically a gap before you get the formal title professor (here in the UK it historically goes PhD student, postdoc, lecturer (the first one of these that is a permanent job), reader, professor; in the US it's a bit different and sometimes you have someone called "associate professor" but not be entitled to use the "Professor" as a title before their name, but there's still certainly a potential gap in the middle).
"Scientist" has many of the above problems but is less of a formal term so could maybe be slightly more widely used e.g. maybe a postdoc or someone working in certain types of industry could be called scientist. But it's still basically a job title so it doesn't work for someone that gets a PhD and then becomes a carpenter. It also has the opposite problem that someone could potentially be a scientist without holding a PhD, so if you specifically want to refer to that then it's imprecise. But it has the much larger problem that it only applies to science! It would be very odd to call someone a scientist because they hold a PhD in modern art or literature, or even mathematics or economics.