They don't look different to the user at the time. The app is listed in the app switcher regardless of whether it is suspended or not running. The app switcher makes no distinction between "it is suspended" and "it is not running but it was running recently".
However, if the user taps the app in the app switcher, what happens next is different. If the app was suspended, it simply resumes right where it was when it was suspended. But if the app is not running, it launches from a cold start, the same as if the user had killed the app and then tapped its icon in the springboard.
For some apps, this difference is quite noticeable. Apple's Books app is a good example; if it resumes from suspension, the user is instantly still reading the same page of the same book, but if it launches from a cold start, it does an involved dance that takes quite a long time, passing thru the library and visibly opening that book, to eventually get the user back to the same book and the same page.
Apple has said that ideally you should write your app in such a way that both situations look identical to the user, by saving state when you go into the background so that you can quickly restore that state the next time the app is cold-launched; but as I've just demonstrated, Apple itself does not always meet that goal.
Another goal is to try to prevent the app from being killed while suspended in the first place. You can't prevent the user from killing the app from the app switcher, but you can try at least to discourage the system from killing the app while suspended. You can't guarantee this but you can try, by not using very much memory for instance, to fly under the radar so that the system will let your app live when it is looking for apps to kill in order to free up resources. Apple has an interesting video on this topic (which would have answered your question), https://developer.apple.com/videos/play/wwdc2020/10078/.