"Shuriken", 手裏剣, literally hand-inside-sword, is just the Japanese name for the same thing. Shuriken and anqi are both small throwing blades/darts that fit inside the hand, that can be hidden in the hand.
I'd say that they're the Japanese and Chinese names for the same weapon.
But don't think "ninja star" when you think of shuriken. Unlike modern ones, historical examples are mostly spike shuriken. Some antiques can be seen at
http://en.wikipedia.org/wiki/Shuriken (and a few more at
http://commons.wikimedia.org/wiki/Category:Shuriken ).
I haven't seen any antique Chinese anqi; perhaps these are different, but I don't think they would be very different. Yang Jwing-Ming's "Ancient Chinese Weapons" and Douglas H. Y. H "Ancient Chinese Hidden Weapons" list a number of Chinese small throwing weapons, various spikes/blades with names like "flying dart", "flying knife", "flying sticker", "flying sting" and star shuriken ("mother-son cross dart"). "Anqi" is a generic terms covering all (or at least most) of these. (Warning: these books are based on literary sources and folklore, rather than historical examples of the weapons.)