Calendar share button?

Tap "Calendars" at the bottom of the screen to bring up the list.

Tap the i button to get info on the calendar you want to share.

Tap "Add Person" to send an email invite to the person you want to be able to see the calendar. They will be sent a subscription link in an email.

If you are trying to share an iCloud calendar, then there should be an "Add Person" option. This will not appear with Hotmail, Google or other calendars. All iOS devices should display the same data for iCloud calendars, as long as the Apple ID in use owns them; i.e, they are not subscribed to from someone else's ID.

Check that the calendar in question appears in iCloud's website to be sure that it is available.

Wait for the server to catch up. It is queuing your request for processing.

Is the Calendar published to iCloud? If it is local only, then it won't work. Check Settings >> Mail, Contacts, Calendars to make sure you are publishing to iCloud.