Texas is divided into informal regions: North Texas, East Texas, South Texas, West Texas. It and a couple other states might be exceptions, but what about cities? Everyone in the area knows what north Dallas is, yet it's also a part of Dallas.

So I disagree with Gary, at least in part.

North US could never be used because it's *the* US, likewise with something like the Rockies. However, there's a North Pacific and South Pacific, but we also just say "The Pacific".

I don't think "East Europe" sounds right any way you use it.

The only rule I see is, northern, southern, etc. can be used to refer to whatever looks to you like the northern part, southern part, etc, while North, South, etc. always refer to something more specific and agreed-upon, usually with set boundaries. The exception is where the terms Northern, Southern, etc are used instead for the specific parts, like Europe.

As far as search engines go, there's a LOT of bad grammar on the web. Try looking up a word misspelled and you get plenty of definitions.