You should tell Webster they’re wrong. And Wikipedia. And Brittanica.
Not to call the editors of those fine resources for elementary school aged children stupid or anything, but the adjective-noun pairs “social democrat” and “democratic socialist” literally imply within the terms themselves what these things are. A democratic socialist is a socialist who uses democratic means. It’s on the tin.
At this moment, you’re on the wrong side of the “First they came for” poem because you’re the one rejecting the Left.