A normal dynamic tweeter may extend into the ultrasonic range. In either case, you'll have to check the specs.
But, since you can only safely get 40mA from the Arudino, you can't directly drive a 4-Ohm or 8-Ohm speaker without an amplifier (or at least a transistor or MOSFET). ([u]Ohm's Law[/u])
A piezo transducer has electrical characteristics similar to a (low value) capacitor and it (usually) has higher impedance at it's operating frequency compared to a regular speaker.
Note that a "buzzer" or "beeper" has a built-in sound generator circuit that makes noise when you apply DC voltage and you can't change the frequency. A piezo "speaker", "tweeter", or "transducer" converts the applied AC signal to sound. You need a transducer. But, if you buy the cheapest thing you can fine on eBay it may not be described accurately.