Google Reader
Google Reader is a Web-based tool for gathering, reading, and sharing all the interesting blogs and websites you read on the web.
It was released by Google on October 7, 2005 and graduated from beta status on September 17, 2007. Is available on any modern web browser with JavaScript enabled.
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Google Currents
Google Currents is an APP that delivers beautiful magazine-like editions to your tablet and smartphone for high speed and offline reading.
It was released by Google in December 2011 is currently available for Android and iOS devices.
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To answer your questions
What's the difference between the two?
R: The major difference is that Google Currents is an APP to be installed on your tablet or smartphone, while the Google Reader is a web-based application.
Is there any reason to use one over the other?
R: The major reason is that Google Current is currently available for tablet and smartphones, while the Google Reader, being a web-based application can be used on every device with an JavaScript ready web browser.
Does Currents replace Reader?
R: Haven't found any indication that Google Currents came to replace Google Reader. Actually the opposite seems to be happening, as the Google Currents can accept your feeds from your Google Reader account. Think of Google Currents as a more flexible way of reading feeds without the need of a web browser.
Reader APP vs Currents APP
You've mentioned on the comment for this answer that there's a Currents app and a Reader app. Yes, it does exists and I didn't know about it.
Just installed to compare the differences:
Reader APP:
Continues to be a plain old fashioned RSS feed, just with a new "face".
From Differences between the mobile and standard web interface (Google Support)
The mobile interface accesses the same subscriptions as the standard web interface, and items read on your mobile device will be marked as read in the standard interface as well. Similarly, items read on the web will be marked as read in the mobile interface. The only difference is that you can't set up subscriptions from your mobile device.
Currents app:
Instead of adding direct RSS feeds, you can add featured sites from well over 150 publishers that Google has partnered with. They include Forbes, TechCrunch, AllThingsD, The Huffington Post, ABC News, Al Jazeera, and The Guardian.
You can choose sites from other featured topics including Business, Design, Science & Tech, Sports, and your RSS feeds from your Google Reader account.
Additionally, you can be a Google Producer and add your own content to Google Currents.