So the 50dma is an average of the last 50 trading days (think 2.5 months), the 200dma of the last 200 trading days (think 10 months).
Because of this, the 50dma moves much faster to price changes than the 200dma...
On the chart, notice that there was a huge drop in price during the middle of the last 200 days. However, the price is almost back to where it was 200 days ago. This makes the line only sag a little between the two red lines drawn on the chart.
If you look at the 50 day blue lines that are drawn, you will notice big changes between them. This makes the lines move much more quickly.
By looking at the chart for the last year the picture is much more clear. Now we see where time intervals (moving averages) get their rate of change.