Никакие дубликаты в SQL-запросе

The problem here is just as you describe: you're checking for the uniqueness of the whole row, your dataset ends up looking like this:

CarItemId    CarId
---------    -----
1            1
1            2
1            3
2            1
2            2
3            3

You want unique CarItemIds with no duplicates, meaning that you also want unique CarIds ---- alright, you have 3 CarIds, which one should SQL Server pick?

You don't have much choice here except to aggregate those extra CarIds away:

SELECT tblcaritem.caritemid, max(tblcar.icarid)
FROM tblcaritem
INNER JOIN tblprivatecar ON tblcaritem.partid = tblprivatecar.partid
INNER JOIN tblcar ON tblcaritem.carid = tblcar.carid
WHERE tblcaritem.userid=72
GROUP BY tblcaritem.caritemid

You could do an aggregate function on the other row... something like max or min

SELECT tblcaritem.caritemid, max(tblcar.icarid) 
FROM tblcaritem 
INNER JOIN tblprivatecar ON tblcaritem.partid = tblprivatecar.partid 
INNER JOIN tblcar ON tblcaritem.carid = tblcar.carid 
WHERE tblcaritem.userid=72
group by tblcaritem.caritemid;

If you put 2 fields in a SELECT DISTINCT query, it will return rows where the combination of the 2 fields is unique, not just where each field is unique.

You are going to have to run 2 separate queries if you want only unique results for each column.