Yes, men and women see themselves differently. Again, gender equality by the metrics they use is largely concerned with material equality. That doesn't preclude social factors from influencing how gender roles are conceptualized and expressed. If what you're interpreting from these studies is true, that there is a natural drive to the exclusion of all other motivators in vocational choice based on gender, there would be uniformity in all cultures across the globe when controlled for material concerns, which a weak correlation at best.

Edit to get lengthy: When dealing with a paper about the relationship between "gender equality" and "sex/gender differences," it is important not to assume that the tool used measured what people think it measures. Gender equality indexes tend to be tools which serve a particular purpose (most often political), and there are many conceptual and operational issues which have been raised by researchers (e.g. see Bericat, 2012, Hawken & Munck, 2013, Permanyer, 2015). As Boulicault points out, we should ask ourselves:

>In other words, is it a valid and reliable way to quantify the phenomenon of gender equality?

>The answer to this question depends on the construct definition, i.e. on how “gender equality” is defined. The UN defines gender equality as the “full equality of rights and opportunities between men and women.” However, between the ten words of this definition lie a plethora of details and complications. What does it mean in practice for men and women to have “full equality of rights and opportunities”? Does it matter whether men and women feel equal or is it enough that they have equal rights and opportunities? Should the equality of rights and opportunities be understood differently in different domains, for example in healthcare vs. politics? These kinds of questions have been heavily debated, leading to the identification of different dimensions and definitions of gender equality.

>These complexities are reflected in the ways gender equality is measured. One reason that so many gender equality measures exist (and that these measures are compound indices rather than uni-dimensional indicators) is precisely because gender equality is complex and can be conceptualized and defined, and therefore measured, in many different ways. As such, rather than seeing all these measures as strictly competing, it’s helpful to think of them as different tools, each suited to measuring different constructs or dimensions of gender equality. For instance, if you want to measure gender equality within social institutions, you won’t want to use the GGGI, which is intended to measure gender equality across four broad domains. Instead, an index like SIGI -- which is specifically created to measure gender equality (and gender discrimination) in social institutions -- would be the better tool for the job. In other words, just like you would use a thermometer over a meter stick to measure water temperature, you would use SIGI over the GGGI to measure gender equality in social institutions.

These indexes tend to measure achievement outcomes in particular dimensions of interest, such as "political empowerment" (think the proportion and distribution of men and women in politics). It is worthwhile to highlight the fact that Guiso et al. (2008) use the GGI, but explicitly think of it as "women's emancipation (GGI)."

There are two things to keep in mind here. First, not all of these dimensions may be relevant to specific outcomes. As Else-Quest et al. (2010) remark:

>Some aspects of gender equity may be more germane to math achievement than others; for example, equal access to formal schooling (at all levels) surely has a profound impact on girls’ math skills, but women’s greater life expectancy is probably less relevant.

Second, there is the issue of the concept of gender itself. For many, the research question is whether sociocultural factors associated with gender (gender attitudes, norms, stereotypes, ...) contribute to societal sex/gender differences in outcomes. As Noll explains:

>Understanding gender norms and stereotypes is critical to understanding why gender equality and gender neutrality are not the same concepts. Norms, attitudes, and stereotypes about gender give people information about what is typical and/or desirable in their social context and influence their preferences, beliefs, and behavior. Psychological research has repeatedly demonstrated that gender stereotypes and norms matter for how people conduct their lives and that they contribute to gender differences, and that gender stereotypes and norms are robust even in societies with high gender equality.

Being more "gender equal" does not necessarily mean that, for example, there are less gender stereotypes, that boys and girls are raised in the same manner, etc. For instance, Breda et al. (2020) argue:

>This means that countries that have eliminated the most the male-primacy ideology or “vertical gender norms” regarding women access to the labor market or even leadership positions are also countries that have developed more “horizontal essentialist norms” regarding women’s and men’s appropriate skills, behaviors, or emotions.

Therefore, countries which are and/or have become more "gender equal" over time do not necessarily have, inversely and for instance, weaker gender stereotypes about boys of the sorts which are related with boys' achievements in literacy (e.g. see Retelsdorf et al., 2015, Pansu et al., 2016, Heyder et al., 2017).