There is alternation of Yiddish and Russian verses, so I added Russian as second language.
Mikhail (=Michael) and Misha in Russian are the same name. The difference is that Mikhail is formal one, while Misha is informal one - just like Robert and Bob or Williams and Bill.
Michael Iosifovich (on Soviet records) and Misha (on Hed-Arzi etc) Appelbaum are really different persons! They even have different spelling in Russian: Эпельбаум vs. Аппельбаум.
May be we should spell M.I. Appelbaum as Apelbaum i.e. with single "p" ? Pavel, you are an expert in Jewish names, what do you think?
Фамилия певца Михаила Иосифовича Эпельбаума всегда писалась с одним "п", так как написано на этикетке представленной пластинки, а не так как в её описании здесь. Фамилия же израильского певца Миши Аппельбаума (Misha Appelbaum) пишется с двумя "п".