My dataframe coordinate system is in UTM with linear unit Meter.
If I have a Polygon shapefile in a UTM coordinate system with a linear unit of Foot_US and I am sent a shapefile in the same UTM coordinate system with a linear unit of Meter. I reluctantly copy/paste the linear unit Meter feature into the linear unit Foot_US shapefile and the vertices' xy are identical in both the linear unit Foot_US and Meter.
What am I missing. I would have figured they would be different.
This is something akin to 'which is heavier, a pound of feathers or a pound of lead?'
The shape is the shape, regardless of whether you describe the lengths in feet or meters. The software is (appears to be, since you don't specify which software) handling the conversion math between the two with the on-the-fly reprojection as ustroetz mentions, so when you copy/paste that adjustment has already been done.
Now if you took your meter shapefile and defined it (not project it) as feet, then things are going to change because you're telling the software the values actually mean feet, rather than it converting between the two. This is where you can run into problems, if your coordinate system is undefined or incorrectly defined. Otherwise the software should know from the projection data what math has to be done to relate the two.
That said, their could be differences at smaller scales/larger areas or when the coordinate systems and datums of the two datasets are different. Rounding errors and other distortions introduced when coverting between the two may cause points not to align. In your case you're using essentially the same coordinate system and datum, you're just changing the unit of measure which is a relatively straight-forward and simple conversion.
Are you looking at the coordinate system's linear unit, or the data frame's display units?
If you can calculate geometry in an attribute, you would be sure of the coordinate system and units used.
(I am guessing that the polygon appears in the same location with reference to a third (geo-referenced) dataset.)
You can select features from one feature class and add them to another feature class using the Append Tool. This will automatically reproject the features when the Spatial References are different.
