yes, both were socialist, but communism was not inherently or intrinsically anti-Jew
Many Jews joined it - and were disproportionately represented in the initial leadership (though not the majority) - as witnessed by Trotsky.
Communism was one of 4 options for Jews in the Russian Empire in the 1800s -- remember that the 1800s was the rise of nationalism and each nation said "this is my land" - the problem being that most demands overlapped
Communism was not anti-Jew during Lenin, not at all
Stalin had some anti-Jewish tendencies but this was exacerbated by the number of Jewish origin communists who opposed Stalin, Grigory Zinoviev and Lev Kamenev against Jewish arch-rival Leon Trotsky, - well he didn't care about who he killed: Jews, Christians, Muslims - anyone was fair game for him.
The Council of People's Commissars adopted a 1918 decree condemning all antisemitism and calling on the workers and peasants to combat it. Lenin continued to speak out against antisemitism. Information campaigns against antisemitism were conducted in the Red Army and in the workplaces, and a provision forbidding the incitement of propaganda against any ethnicity became part of Soviet law. State-sponsored institutions of secular Yiddish culture, such as the Moscow State Jewish Theater, were established in Soviet Russia and the Soviet Union during this time, as were institutions for other minorities.
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The Soviet murder machine differed from the Nazi one in that the Nazis killed Jews, Slavs, Gypsies, priests, communists while the Soviet murder machine killed everyone indiscriminately (equal opportunity murderers the old Bolsheviks were)
“yes, both were socialist, but communism was not inherently or intrinsically anti-Jew”
Yes and no. Yes in that it’s not intrinsically anti-Jew in the sense of not wanting any Jewish ethnicity in there, no in that it actually is intrinsically anti-Jew in terms of religion and culture, as Karl Marx himself was at the very least a self-loathing Jew if not a full-blown anti-Semite DESPITE having even more Jewish blood than Hitler himself was rumored to have, advocated separating Jews from their culture and beliefs, and outright compared Jews to con men in his infamous “What is Judaism’s god? Money! What is Judaism’s religions? Huckstering!” line, and even advocated for a full-on extermination campaign against lesser beings in the revolution.