As previously discussed, both mourning and Chol Hamoed share a prohibition of shaving. Yet the reasons for such are very different; the prohibition to shave for a mourner is an expression of that mourning, whereas the prohibition of shaving on Chol Hamoed is a decree meant to ensure all would shave before Yom Tov. The former aims to make one look disheveled, while the latter aims to ensure we come into Yom Tov properly attired.
Yet even within the different laws of mourning, it is possible that the same prohibition reflects differing, even if complementary, motifs. "Our Rabbis taught: these are the things a mourner is forbidden from doing...he is forbidden to read the Pentateuch, Prophets, or Hagiograplia, or to recite the Mishnah, or Midrash and halachot or the Talmud or Aggadoth" (Moed Katan 21a). A very similar teaching is recorded regarding Tisha B'Av, the national day of mourning of the Jewish people. "All the restrictions that apply to the mourner hold equally good on the Ninth of Av. It is also forbidden to read the Pentateuch, the Prophets, and the Hagiographa or to study Mishnah, Talmud, Midrash, halachot, or Aggadoth" (Taanit 30a).
However, the prohibition of Torah learning on Tisha B'Av and that of a mourner may not be identical. Regarding Tisha B'Av, we are taught that "he may read such parts of Scripture which he does not usually read, and study such parts of Mishnah which he usually does not study; he may read Lamentations, Job, and the sad parts of Jeremiah; and the children do not study, for it is said, 'the precepts of the Lord are right, rejoicing the heart" (Tehillim 19:9).
These two leniencies--learning new material and learning sad material--and the stringency forbidding children from learning are mentioned only by Tisha B'Av, and do not appear vis a vis mourners. Some claim that the Gemara felt no need to mention all the details twice, and just as one may learn new and sad material on Tisha B'Av, one may do so during the week of shiva. Others claim the Talmud is quite precise, and these leniencies were not mentioned precisely because they do not apply to a mourner. While this may not be the accepted view in practice, I would like to articulate the logic behind this view.
It is because Tisha B'Av is rooted in the sadness of the day that the Gemara permits one to "read such parts of Scripture which he does not usually read, and study such parts of Mishnah which he usually does not study". At first glance, this seems quite odd. As Rashi explains, when one learns something for the first time, it is often difficult to comprehend the material leading to tza'ar, pain. The joy of learning comes only after putting in much hard work.