Yes, they are both commonly used momentum indicators, but how they are calculated and/or interpreted is quite different. The Chaikin money flow oscillator is similar to the MACD indicator in that it uses two different exponentially weighted moving averages to analyze momentum. In the case of the Chaikin Money Flow, the indicator uses the difference between a 3-day exponentially-weighted moving average (EMA) of the accumulation/distribution line and the 10-Day EMA of the Accumulation/Distribution Line.
As you can see from the chart of Amazon.com Inc (AMZN) below, negative money flow as shown by the period between the two red rectangles suggests that the directional bias is downward. Positive money flow is marked by the green areas on the indicator and suggests that the trend is upward.
The money flow index is quite different than the Chaiken money flow index in that it uses volume in combination with recent price movements to determine whether momentum is up or down. Many traders view this indicator as a volume-weight relative strength index (RSI).
As you can see from the chart above, the money flow index never moves above or below key overbought or oversold levels on the chart of AMZN like it did in the Chaikin money flow example above. When using the money flow index, buy and sell signals are only generated when the index moves beyond the 20 or 80 levels. Since the underlying indicators used to create these indicators are different, it is unsurprising to see that the buy and sell signals are quite different. In general, It is important to understand the underlying formula of any technical indicator before using it to generate buy and sell signals.