They're writing a report, I'd say; it's a direct response, intended (I assume) only for a select cadre of people. In this case, military personnel writing about what they've experienced, and only the military'll read it. So, a report.

Students are asked to write how they feel after the military training. Here are three possibilities: => The students are writing down their feelings and impressions about the military training they've just received. => The students are writing about their military training experience they've just completed. => The students are writing an essay about the military training they've just received.