My pleasure. So just as a reference, the image is included here. The green line is the regression curve which is the middle Andersen Bands line. The red curve is a moving average which is the middle line of BB. The two vertical lines are the look-back evaluation period in calculating the regression and average values at the time where they intersect the vertical line on the right. This is shown by drawing the regression line (blue) and average (magenta).
If you were to keep the same distance between the vertical lines and slide them backward you would see the blue line ending on the green line for each of the bars as well as the corresponding magenta line ending on the red line.
The image shows that as you would slide these forward when price began transitioning higher, the average (red) was much slower to turn up than the regression curve (green).
Consequently the price variance around the magenta line and between the vertical lines reflects what becomes standard deviation around the red line at the point where it intersects the right vertical line, which is the basis for Bollinger Bands. It only looks at volatility around the average without bias for direction.
Andersen Bands also calculates volatility between the vertical lines. However, volatility is measuring dispersion around the blue regression line. This line is a "best fit" line, different than the average, it draws a line through the middle of the data (between the vertical lines) such that there is equal amount of dispersion above and below it. As a consequence, direction is accounted for and the volatility is thus measuring the quality of the regression line as a descriptor of price action. The tighter the bands the stronger the trend. At the same time Bollinger Bands would become rather wide because price is moving away from the average faster than the average is moving. Hope that helps.
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