Thanks for any help!!
In German language, "Z" is pronounced like English "ts", and "S" is pronounced like English "z". So a German reader would pronounce “Saytzeff” close to his Russian name, Зайцев.
So “Saytzeff” is close to German phonetic to his (Russian) name, while Zaitsev would be transliteration of it, or writing it in a way so English-speaking reader can pronounce it close to the sound of his Russian name, Зайцев.
IOW: “Saytzeff” is a version for audience speaking German, "Zaitsev" is for English-speaking one.
The rule is named after the Russian chemist Александр Михайлович Зайцев. He studied in Germany and wrote most of his papers in German, spelling his name consistently as “Saytzeff”. Zaytsev or Zaitsev are English spellings of the same name. Actually, there is a case for spelling Russian names the way their bearers did themselves when they used Western languages.