Bluetooth 4.0 vs. Bluetooth LE, is there a difference?
They're not the same thing

From the Wikipedia article on the Bluetooth specifications:


  [Bluetooth Core Specification version 4.0] includes Classic Bluetooth, Bluetooth high speed and Bluetooth low energy protocols.


Getting a Bluetooth LE device or chip does not mean it will work with Bluetooth Classic. From the Bluetooth LE Wikipedia page:


  The Bluetooth 4.0 specification permits devices to implement either or both of the LE and Classic systems.


So you can have a Bluetooth 4.0 device that does not support Bluetooth LE or only Bluetooth LE. That's not the least bit confusing. I'm imagining a lot of shrugs and "eeehhhh..."s went into writing the specification.

I've only seen the BLE abbreviation, and it's the only one listed as an alias on the Wikipedia page. So use BLE.