Noise is a disorderly move. It doesnt need to be volatile. just erratic and unpredictable.
When prices move from point A to point B in a straight line. there is little or no noise. When prices move with an erratic path. going up and down before reaching point B. there is noise.
Noisy markets should be traded with a mean reverting strategy - using oscillators. perhaps. Markets with low noise should be traded with trending methods - moving averages will work well here.
While it will never be possible to exactly determine when a market is exhibiting high noise and when it is exhibiting low noise. one simple method is to check price movements with moving averages. If moving average strategies are making money consistently. then the market has low noise. If a momentum oscillator like Rsi is catching the highs and lows in prices then we have a market with high noise - do not use trend indicators here.