When Lag b’Omer occurs on Sunday, the Rema writes that one may cut one’s hair on the previous Friday in honour of Shabbos. Those who follow Minhag Vilna observe the mourning laws of sefirah until the morning of 3 Sivan. From the case of Lag b’Omer, we can possibly derive that should 3 Sivan occur on a Sunday, one may cut one’s hair on the previous Friday.   

In the case of sefirah, the Shulchan Aruch  (Orach Chaim 493:2) uses the word “lehistaper” (haircutting). However in the case of Chol Hamoed the word “megalchin” (shaving) is used (Orach Chaim 531:2). Why the difference in wording for the same actions? It is possible that the reason is that the third perek of Moed Koton which includes the subject of cutting any human hair on Chol Hamoed begins with the words “v’ailu megalchin”.