What's the difference between mixer and modulator?

mixer and modulator have the same math equation, but what are the difference between both?
Please describe the difference in details as possible.

Hi:

I think the mixer is typically a four quadrant multiplier producing the Double Sideband Signal, but a modulator would consist a combination of a mixer, phase shifters, VCO and Adders/subtractors to obtain the desired single sideband signal.

Rgds

In most RF modulator, the mixer is the key components. Mixer is used to transfer frequency from one to another. Modulator means it will modulate the signal with information from one to another.

Yibin.

There are two input in this circuit.
One is large signal and one another is small signal in mixer.
The two signal are small in multiplier.
The two signal are large in modulator. (I am not sure.)

To by more precise: the mixer and the AMPLITUDE modulator have the same math equation.
Hence, not every modulator is a mixer .

Can I use a mixer as a Amplitude Modulator?
Or use Amplitude Modulator as a mixer.

In my opinion yes, but with reservatons.

1. All devices are designed to perform their function.
2. Such parameters as input levels may be critical.
3. In case of balansed mixer only the side bands are at the output (without carrier).
4. the list may be continued........