I am very confused about the prohibition of shaving. The Shulchan Aruch uses the term "L'histaper" which means cutting hair. There is no term "giluach", or shaving, used by either the Shulchan Aruch or Mishnah Berura for being prohibited during sefirah. Why then is shaving prohibited during sefirah?
Masekhet Semachot (7:11) in regards to mourning writes that lihistaper means to cut the hair of one's head, mustache, beard, and all other hair.
Nitei Gavriel (Pesachvol 3, 49:2) and Chazon Ovadyah (p. 262) write that including in the minhag not to take a hair cut is not to shave.
And as sam pointed out in a comment, the Mishna Berura forbids shaving at all times, so it wouldn't make sense to mention it about sefira.
I don't think there is any real significance to the fact that the term "giluach" does not appear in the Shulchan Aruch. It is mentioned by rishonim (e.g. Rabbeinu Yerucham נשארו לד' והם לג' שלמים ומגלחים בבקר של ל"ד כי מקצת היום ככלו), and a simple comparison of the Rema in Shulchan Aruch to the Rema in Darchei Moshe will show that in the former he speaks of "lehistaper" regarding the same halachos that he speaks of "legaleach" in the former. In other words, it is lav davka (imprecise).
For example, regarding the case where Lag B'omer falls out on Sunday, in Shulchan Aruch he writes:
מיהו אם חל ביום ראשון נוהגין להסתפר ביום ו' לכבוד שבת
Yet when discussing this same case in Darchei Moshe he writes:
כתב מהרי"ל אם חל ל"ג בעומר באחד בשבת אסור לגלח בערב שבת אבל מהר"י וייל כתב דשרי
Chida, in Shut Chayim Sha'al (1:6):
"One who looks carefully at the origins and roots of this matter… that this custom is very lenient… and for any reason we may override it… According to the straightforward understanding, we have no proper or sufficient reason to prohibit shaving." (See also Rav Sperber's Minhagei Yisrael, vol. 1 chaps. 12-13.)