Can you provide a practical example illustrating the difference between SEM and standard deviation?

Imagine testing students' math abilities. The standard deviation of their scores reflects the spread of scores *around the average* of that group. SEM, however, reflects the variability of a *single student's score* around their true math ability. A student might have a high standard deviation (in a class with diverse abilities) but a relatively low SEM (if the test is reliable and measures their skill precisely).