That is the difference. While having proven Jewish ancestry, or being married to a Jew ,does not mean you would be considered a Jew under Orthodox Judaism , having the ancestry ( Jewish father, grandfather) does allow you Aliya under the law of Return. The Law of Return allow for only the immediate family of a Jew, as in the case of a Jew married to a non Jew and their children but not the non Jewish grandmother. These Ethiopians converted to Christianity long ago and left the Jewish fold, many intermarried, making some ineligible for Aliya. The Russians had the same questions asked at them and all that did come came under the law of Return and all it's rules applied to them.
Israeli soldier lightly wounded after being hit by car south of Hebron (Haaretz)