"Trail running" shoes differs markedly from "road running" shoes and "track running" shoes. I can understand these categories. But I also found an event entitled "Cross Country Running Event". Can the "Cross Country Running Event" be treated as "Trail Running Event"?
Cross-country races are largely run on trails of all sorts, ranging from hard-packed dirt to gravel. Depending on the course, you may even hit some pavement along the way. In general, though, you can treat cross-country running as a trail event.
Note on usage
Trail running is used to indicate any running not done on the road or pavement. Cross country usually refers to the organized sport of running 5k/8k/10k distances off-road. If someone says, "I run cross country", then, more likely than not, that person is on a team and races regularly. Someone who says, "I'm a trail-runner", runs on trails but not necessarily competitively. And you would probably be hard-pressed to find "Trail Racing" or "Trail Running Racing"! Rather, it's almost always "Cross Country Racing".
*Hard-core runners will normally race the course in spikes (metal or rubber) for added traction and speed. Regular trail shoes are way too heavy for racing (13 oz versus 8 oz). Of course, your choice of shoes would depend on your goals or the level of the event.