Can you upload a backup from one type of Apple device onto another?

I feel like this is probably a dumb question but is one that can easily be answered! If I backup my iPad onto my computer, am I able to install the same backup onto an iPhone? I'm about to get a new iPhone 6 and would like to put all of my apps, messages, photos, etc. From my iPad onto it once I get it.

If the phone shares the same account then yes. Some apps on ipad are ipad only apps though, all iphone apps run on ipad but specific ipad apps do not run on iphone.

Should be able to. Of course iPad specific things wouldn't transfer over.