In one technical sense, 'Ashkenazi' means Jewish and descended from specific communities that settled in what is now France and Germany during the first millennium. In casual usage it's broader, meaning Jewish and of European descent (as opposed to Middle Eastern or North African). Most of the European Jewish communities between the Rhine and the Pale of Settlement descended from those same Western European communities anyway.
'Sephardic' technically indicates adherence to a set of religious and cultural traditions that are different from those of European Jews, but in casual usage it indicates ethnicity or geographic origin. 'Jewish and of Middle Eastern/North African descent'. 'Mizrahi' is a more technically appropriate term for a Jew whose recent ancestors are 'Eastern', which is how it literally translates.