Great, thanks! We actually go into more detail in the courses on this topic, but given what you have, first reference page 337 and read through the Logical Opposition section (and when reading that section, keep in mind that Could be True is like Some, and Not Necessarily True is like Not All).
Next, Could be True and Not Necessarily True are both quite similar and quite different! If we were to use the Constructs that appear in the LRB and use a "truth" scale of 0-100, we'd see something like this:
Must Be True = 100 (all of the truth)
Not Necessarily True = 0 to 99 (everything but Must Be True)
Could Be True = 1 to 100 (everything but Cannot Be True)
Cannot Be True = 0 (none of the truth)
Using those definitions, Could and Not Necessarily look really similar—they overlap for the most part (from 1-99). But, at the same time, they include each other's opposite (Could includes Must, and Not Necessarily includes Cannot). So, they often cover the same ground—the middle ground where things might be true—but at the ends of the spectrum (Must and Cannot), they differ significantly.
Another way to see how they differ is to realize that Not Necessarily True is identical to could Be False. So, comparatively, one term is Could Be True (there exists a possibility something is true, but it doesn't have to be) and the other Could Be False (there exists a possibility something is false, but it doesn't have to be)
It's a subtle yet definite difference, but the good news is that you aren't typically tested directly on the difference. Please let me know if that helps. Thanks!