I am trying to help a friend in another part of the country diagnose this problem. She has a background layer from google and has a vector layer overlaid on it. It looks fine in the composer but when printed the layers are scaled differently and don’t match.
QGIS version2.8.2 but she is going to upgrade to 3.2 now that is officially stable.
As can be seen from the screen shots the project CRS is 3857 and OTF enabled which should take care of the vector layer which is probably 2193.
QGIS main window