The point is that in America almost all cars have automatic transmission, whereas in Europe the majority of cars don't.
Americans tend to refer to non-automatic transmissions as "stick-shift". "Foreign shift" seems an unusual expression for this.
It might refer to the gear lever position. I understood most American manual transmission cars to have had column shift, whereas the Italian car's gear lever is probably floor-mounted. I have no idea how much difference this makes to drive.
Even if when both are "on the floor", the gears are sometimes in a different position.
I used to switch between a German car that had
R 2 4
1 3 5
and an American car that had
You don't want someone putting it into Reverse at a light out of habit.
Up through the 1980s at least, most cars were available in both automatic and manual transmission. I remember test-driving some new cars in 1987 with manual transmissions. It would have been very common in 1968 to teach someone to drive with both automatic and manual transmission.