I have 2 iPads. Should they both have the same id? I got a new iPad and gave my daughter the old one. She is unable to get on it using the password and ID I gave her. So I changed the password on mine -she still can't use that password- is it different on all devices and I forgot it?
No, your Apple ID email/password combination will be the same everywhere - on your iOS devices, computers, and online. You can use it on as many devices as you would like and it will always work just fine - regardless of the device. 

Unrelated to that though, I would consider setting up a new Apple ID for your daughter and then configuring Family Sharing to link the two. Apple IDs are very much designed for one user per Apple ID. 

Aside from that, make sure you are entering the Apple ID username/password combination correctly and it will work.