When Wollstonecraft talks of unnatural distinctions between men and women, she's referring to those artificial differences imposed by custom and tradition. Natural distinctions, on the other hand, are those arising out of the biological differences between the sexes. One such example, according to Wollstonecraft, is the "natural affection" that makes women good wives and mothers but which they are prevented from displaying by a want of virtue arising from a lack of independence.
Examples of unnatural distinctions could include the respective roles that men and women play in society. In Wollstonecraft's day, men were expected to be the bread-winner while women stayed at home to look after the children. Wollstonecraft believes such an unnatural distinction to be grossly unfair. She argues that if women were able to pursue careers like men, then many of them might be saved from what she calls "common and legal prostitution."
By "legal prostitution" Wollstonecraft is referring to the situation in which many women found themselves in her day: getting married to men they didn't love simply in order to have a stable home life. Such a distinction is unnatural because it isn't based on the innate characteristics and talents that women have and which they could use to achieve true independence, if only they were allowed to. Distinctions such as these are imposed on women by a patriarchal society which seeks to maintain men in a position of power and authority.
Though things have changed an awful lot since Wollstonecraft's day, there's still a long way to go towards achieving genuine equality between the sexes. The gap in pay between men and women continues to be a persistent problem, as does the common prejudice that certain careers—such as science and engineering—are somehow not suitable for women. Wollstonecraft would certainly have described these as examples of unnatural distinctions and would've challenged them with the eloquence, vigor, and determination for which she was famous.