This is a difficult question to answer practically but conceptually it's easier to see. So let's start with the concept. A correlation of 0.38 means that performance on one test predicts performance on the other by this factor of 0.38. What does this mean? If there was a correlation of 1 between the two tests, then performance on one can completely predict performance on the other. This could mean that the tests are measuring the same thing, or, in other words, the same thing causes you to score identically in both tests. If there was a correlation of 0 between the two tests, then performance on one cannot predict performance on the other at all. This means that they're measuring different things, or, in other words, that there likely isn't a common factor determining performance on both tests. Anywhere in between and you get the intermediate: performance on one test partly predicts the performance on another, meaning that there is overlap in terms of what causes your score on the tests.
Practically, it's harder to determine what any correlation coefficient means and it's field-specific. In some biological and psychological disciplines, correlations of 0.3 or so are still considered effects because due to the complexity of biological systems, no one factor can completely predict another factor. In other words, even if you smoke a pack of cigarettes every day for twenty years, that cannot completely determine that you will get cancer. Your odds go up, but it's not a certainty. There's just a lot of noise in biological systems due to the interaction of multiple variables. But in fields like chemistry and physics, you'd be laughed out of a room if you try to show a correlation of 0.3. Our correlations are usually 0.9 and above, generally 0.99 or so for direct measurement of physical effects. We're only limited by the precision of the instruments we're using - noise in the system is usually far below that precision. So practically, your question is hard to answer but conceptually, it's pretty clear cut.
