I have 2 files added to my map of Oregon: an Oregon hillshade (.sid) layer, and a .shp file that consists of about 20,000 monitoring points. The hillshade layer was added first and therefore the map/data frame takes on the same projection as the hillshade layer (NAD 83 Lambert Conformal Conic). The Geographic coordinate system of the points is different (NAD 83 2011) from the GCS of the hillshade layer. So, in order to make the coordinate systems match, I go to the Define Projection tool and change the point layer to match the hillshade layer by selecting NAD 83 Lambert Conformal Conic from the list. The map then redraws and my points are now positioned to the left of the state and also scaled very small.
I've done a ton of reading on datums, projections, GCS vs. PCS, etc. but I don't understand what is happening here. Can anyone help?