I've seen both refered to as IPA, which is the real IPA and how are they different?
Most often, if you see IPA, it's an "India pale ale".
"Imperial pale ale" is an informal, descriptive style (i.e., a strong pale ale), whereas "india pale ale" is a BJCP recognized style. India pale ales are primarily understood as a hopped-up version of a pale ale, made to withstand long travels. Beers with an "imperial" nomenclature (typically synonymous with "double") are brewed to be a stronger, higher ABV -- think double IPAs, imperial stouts, etc.
[English] India Pale Ales (BJCP Style 14A) were shipped to India (and elsewhere) during the late 18th Century.
[American] India Pale Ales (BJCP Style 14C) are significantly different.
Imperial Pale Ales (BJCP Style 14C) refer to a relatively stronger (in alcohol) beer. They are a modern invention by American Craft Brewers.
The "Imperial" part of the name though, has some interesting history.
During the 1698-1700's "Porter" beer was exported from England to the court of Russia. However during initial shipment, the long journey ruined the beer. Barklay's Brewery in London significantly increased both the alcohol and hops in the beer to help it prevent spoilage during the trip. This beer became known as "Russian Imperial Stout".