Align Edge not creating coincident boundaries

[MattSk]

I recently started a GIS class and am experimenting with my own project using Align Edge, but it's not working.

I've imported kmz files I made in Google Earth. Some I've converted to shapefiles. Because I manually made these polygons their boundaries are not flush, so I'm using the Align Edge and Align Feature tools. But that doesn't work, as it leaves a buffer of about 10 ft, and it shifts both polygons boundaries around. 

I suspect a topology issue... maybe with an M or Z coordinate? A Google search provides no answers.

I strictly want to keep one polygon stationary, and align the new polygon to the stationary one, but both tools don't operate that way. 

[MattSk]

Example of gap it leaves when using Align Edge.

An example how I'm using Align Feature:

But it shifts it purple polygon and the light polygon to the right:

[DanPatterson]

use featureclasses in a locally stored file geodatabase for testing

shapefiles don't support topology (see `limitations` section

Shapefiles in ArcGIS Pro—ArcGIS Pro | Documentation

inputs also need to be in the same coordinate system