I’m going to assume your device is fairly new or that you purchased AppleCare recently. I use Apple’s upgrade loan program which includes AppleCare and when I first got my phone that‘s what I saw in Settings as well. It takes about 72 hours after the phone is activated or the AppleCare is registered for that setting to update and reflect your correct status. It will change to display the expiration date, 2 years from now, of the service. You will get an email with the AppleCare agreement about the same time, maybe a bit before, the setting updates. The reason you see that last screen is that the device is already covered by AppleCare so purchasing it is not available.
In the past I never took notice of this because prior to a later version of ios 12 that warranty/AppleCare status was not shown there so I wouldn’t have been confused.