Da das OP eine ernsthafte Anfrage ist, möchte ich es wieder auf die erste Seite schubsen, wenn ich auch nicht zur Antwort beitragen kann.

But is it the same as in Germany where you just lift your hand off the steering wheel (not really waving it)

Yes, that's what it is. No actual waving, just a friendly lifting of one's hand.

I didn't know it was called a courtesy wave. Interesting :-)

In my car, it's just a simple lift of the hand while repeating the mantra "Thank you, thank you, thank you". In New Jersey there aren't many opportunities to give a courtesy wave ;o)

@ #5

I try to avoid cars with NJ license plates here in VA. ;-)

I totally understand, Rex. I am from PA originally and am now surrounded by these crazies ;o)

Out here on the left coast it's also a lifting of the hand. Occasionally there might be a salute, but no real wave. And yes, the mantra of "Thank you, thank you, thank you".

When trying to get into a line-up of cars, sometimes people will put their hands together in a gesture similar to Duerer's "Praying Hands". (I know, OT)

It's also used on two-lane highways out in the country, when a slower driver pulls over onto the shoulder temporarily to let you pass. We actually expect that as a matter of courtesy, down here where there's more space and less traffic, and we expect the hand in acknowledgment. But it's just lifted near the rearview mirror so it's visible, not moving; I don't know that I'd really call it a wave.

But if the fast driver behind is going too fast, or actually tailgates us (or, heaven forbid, flashes headlights in that pushy European way), then we may be inclined not to. There's a fine line between seeming to demand that someone pull over, and politely intimating that it would be helpful if they would. (-:

And in California, the vehicle code requires that slower cars on two-lane roads pull over at the first opportunity to let faster cars go by, if there is a queue of 5 or more behind the slower car. Cars will sometimes beep their horns in passing as a thank-you. (A "courtesy beep"?)

#9 (or, heaven forbid, flashes headlights in that pushy European way)

Hey, hey, was sind das hier für Pauschalisierungen!? ;-)

Nur mal OT so nebenbei: Auch wenn's hierzulande leider gelegentlich gemacht wird, es ist ziemlich verboten. Gilt nach meinem Wissensstand vor dem Gesetz als Nötigung.
Ich persönlich würde es sogar als Morddrohung bezeichnen, wenn so ein Raser sich einem mit Tempo 200kmh zwei Meter hinter die Heckstoßstange klemmt.

Leider ist in diesen Momenten meist kein Polizeiauto weit und breit zu sehen. Schade. :-(

Thank you all for your helpful replies. Much appreciated. :-)