Apple ID's -- I have apple id's on two devices
Yes, you can absolutely have multiple devices using the same Apple ID and have different apps and the same apps installed on them. What apps are installed on each device is managed by the individual device and/or by iTunes when you sync.

There are not many games or apps that allow for sync'ng across multiple devices though, so for most apps the content will be unique to each device. Hopefully the developers will catch on that many of us are using their apps on iPhones and iPads and get them to sync.