S1TBX 8.0.6: I observed that Terrain-Flattening and Terrain-Correction of Sentinel-1 using auto downloaded Copernicus 30m DEMs was not the same as using a Copernicus 30m DEM as an external DEM. Auto download is introducing a 1/2 pixel and 1/2 line shift to the DEM. I verified this by manually shifting the external DEM by that amount. I obtain the exact result as auto download with the external DEM after shifting the georeferencing by the 1/2 pixel and 1/2 line: (0.000208333333333,0.00013888888888).
My test data is north where x and y pixel size is different: N51E095.
Pixel Size = (0.000416666666667,-0.000277777777778)
The georeferencing adjustment that produced the same result as autodownload is coincidentally on the even lat/long:
gdal_edit.py -a_srs EPSG:4326 -a_ullr 95 52 96 51 Copernicus_DSM_COG_10_N51_00_E095_00_DEM.tif
The original DEM corner point is: 94.999791666666667,52.000138888888891
Additional testing needs to be performed in more equatorial areas to verify this holds true.