There is a difference between לא תשיג and לא תגיע ידו (his means suffice not), just as there is a difference between השגה and הגעה: השגה (obtain/achieve) is an action done in the act of acting and is associated with the word את which obtains the matter. And ההגעה (arrive) is actually the action and is associated with the word אל which comes to the matter. And thus, it always uses the language השגה to talk about lack of attainment. And when it uses the language הגעה, it is saying that he reaches the matter but nevertheless still does not have it, since he is poor and needs to sell it.

And with respect to a woman giving birth, it uses לא תמצא ידה (And if her means suffice not)⁶⁷⁵, since her husband brings the sacrifice for her and she neither משגת nor מגעת, but only מוצאת (finds) through her husband.

footnotes: ⁶⁷⁵ Leviticus 12:8.