Is there any halachik difference between shaving (completely) one’s pubic hair and merely trimming it (not shaving it off completely) for a man?
It is not permitted to shave the pubic area for cosmetic and beautifying reasons, even in a partial manner.
The Torah prohibits a man from beautifying himself in the manner of women, and it is therefore prohibited to shave one’s body in places that it is the way of women (and not men) to do so.
The Talmud (Nazir 59b) specifies pubic hair and armpit hair as being prohibited for men to shave. According to Rashba (Vol. 4, no. 90; see also Beis Yosef, Yoreh De’ah 181, and Bach 181:8-9), this prohibition applies to the entire body. However, the Rambam (Idolatry Chap. 12:9) writes that the prohibition (in his opinion, rabbinic) applies specifically to places that it is the custom of women alone to shave. This is also the ruling of the Rema (Yoreh De’ah 182).
Therefore, if it is generally accepted for men to remove hair in a given part of the body, it is permitted to do so. For parts of the body where it is not generally accepted for men to remove hair, it is forbidden to do so for the sake of beautification, but it is permitted to do so if one requires this for purpose of medical treatment, or other non-beautifying purposes (see Darchei Moshe, Yoreh De’ah 182, concerning shaving arm-hair for somebody who is ashamed; see also Tosafos, Shabbos 50; Iggros Moshe, Yoreh De’ah 2:61; Seridei Eish Vol. 2, no. 40 — the final two sources refer to the prohibition of coloring one’s hair, and write that it is permitted for non-beauty purposes).
Note that according to several authorities, the concept of something that is “generally accepted” to do is defined by the ways of Jews, and not by non-Jews.
Therefore, if the purpose is for the sake of beauty and attractiveness, it is not permitted to shave body hair in parts of the body where it is not common practice for men to do so (according to the Vilna Gaon, moreover, even the practice of men is not sufficient to permit this, but most authorities are lenient where it is practice of men).
Therefore, it is not permitted to shave body hair for the purpose of beautification, unless it is the common practice for men to do so. For most body hair, it appears that the general practice of men is not to shave hair, and therefore this is to be avoided. This is certainly true for pubic hair.