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Monostable will generate only one pulse; astable will generate a square wave.
In other words, monostable=one-shot, astable=free-running.
And 555 (indicated by Rectifier) is a very good example of both modes.
I think that Jeffttan says true. A monostable multivibrator needs a trigger signal to produce an output pulse, but an astable multivibrator runs and needn't to be triggered for every output pulse. We can say that an astable multivibrator is an oscillator.
with the monostable you can use just one position. high level or low level. if you have low level you can use high level for once accordind to your input signal. you can vary the time for the high level by using a rc circuit. time is proportional with "r*c".