what is the difference between AGC and Limiter?

The AGC keeps the system linear. Limiters do not. For some cases, like constant envelope modulation, the limiter has the advantage of suppressing weaker signals and improving the SNR.

The AGC is a feedback system and so has a delay time. The limiter is instantaneous.

Do you mean the "weaker signals" is noise?

The limiter pushes the weaker signal or noise an extra 6 dB down. For noise it is the in phase part that gets eliminated. The quadrature component is still there and affects angle modulated signals.

This limiting action is why FM broadcast receivers have capture ratios that are only a few dB.

[edited additions. The removal of the in phase noise does some good since many hardware angle demodulators are sensitive to signal level.]

The difference is the time domain: a limiter is nothing but a clipper and manage a sinusoidal wave in different manner for different times accordin to its instantaneous amplitude (like a clipper).An agc is something else: it can evaluate or predict the amplitude and manage the amplification according to the amplitude: in this way different Dt of the hypotetical sine wave are amplified by the same amount of gain (in the steady state response).
Bye Mrm

So, Limiter is faster than AGC, and could improve SNR of system.

Why do we use AGC?

AGC is used on systems that work with signals with the data or information modulated onto the amplitude of the sinewave. Analog examples are the standard AM broadcast band and television. A digital example is QAM.

AGC is also used in signal generators to keep the output level at a known value. This known value is then attenuated down to other known values.

A limiter can be used in a communication systm which employes non linear modulation,like FM. It cannot be used for systems like qpsk , AM where linear modulation is employed.

Limiter gets rid of AM, but AGC can keep both AM and FM

Even if a modulation doesn't implies amplitude information (Like a PSK), the use of a limiter (clipper) should be avoided. This because even amplitude has a part of information during demodulation process whenever source and receiver are not well triggered (frequency speaking) and durig best symbol time recovery process. So before using a limiter investigate the whole demodulation process, not only the modulation type.
Bye Mrm