iPad - multiple users on one account
The term "AppleID" is being used here to refer to two different accounts and that's where it gets confusing.  Your actual Apple ID is what logs you in to the App Store, has your credit card linked and keeps track of your purchases.  The details are in the Settings App under "iTunes &amp; App Store".  As @Gabkano said you can now use Family Sharing to put your kids' Apple IDs under yours so that if you buy an app, song, movie, etc they get it too without having to pay for it again.

But that's not why you and your kids are seeing each others' photos, contacts, iMessages, etc.  Those are all part of your iCloud account which also includes calendars, reminders, Safari bookmarks, and, if you've enabled it, password saving through Keychain.  The login details for that are in the "iCloud" tab of the Settings app just above the AppleID tab.  

Most people use the same e-mail address for both the AppleID and the iCloud ID but you don't have to.  For example, my wife, kids and I all share a single AppleID but we each have our own iCloud accounts.  That way we only have to buy apps once but my contacts and such stay separate from hers and from the kids'. I also log my iPhone, iPad and Mac into my iCloud account so that all of my data is synced between them automatically. 

To make matters even more confusing there's a third account that often gets lumped in with the AppleID: your Game Center ID, which tracks scores and achievements in games.  Your kids will almost certainly want their own GameCenter IDs so I suggest using the same email address there as your iCloud ID.  

Maybe this will help:
&nbsp; Me: &nbsp; AppleID=us@me.com, iCloud=dad@me.com, &nbsp; GameCtr=dad@me.com
&nbsp; Wife: AppleID=us@me.com, iCloud=mom@me.com, GameCtr=mom@me.com

With Family sharing you can set up individual AppleIDs for everyone and link them together but for years I've been doing it the way I explained above and it's worked out very well. 

I hope this helps.