I was finally able to access the webmap and that allowed me to determine why you were getting different results.
The two walk time polygons are created from a slightly different starting point. For any given point, the tool needs to find the point that is closest to the street network, and then the tool calculates how far it can travel in 20 minutes from the starting point on the street.
For your analysis, because the two starting points are slightly different, they end up being located on different portions of the street network and so produce different results.
In the screenshot below one of the polygons is created from the magenta colored point which ends up being located on Villa Oak Dr (since that is the closest location from that point). The green colored point ends up being located on the walking path in the park.
The green colored point is able to travel a lot less number of streets in 20 minutes as compared to the magenta colored point resulting in different walk time polygons.
Hope this helps
Deelesh