Adobe Photoshop (Photoshop for short) is the original product. It has been in use since 1990, more than 20 years! That's a pretty long history for any piece of software. It is the original photo editing program that other photo editing software companies based as their products on. Photoshop is the application professionals use to edit their pictures, create web page designs, prepare images for a printing press, even create images entirely from scratch, and more. Over those 20+ years, many improved versions of Photoshop have been sold. Currently (2014) you can purchase Photoshop Creative Suite version 6 (also called Photoshop CS6) for $699 retail (one time) or an individual Photoshop Creative Cloud (or Photoshop CC) subscription for $19.99 per month (on-going). Buy this version if you need the ultimate in control over editing your images, but be prepared for a steep learning curve.
To learn more about the features of each of these excellent photo editing applications, visit the Adobe website.
Adobe Photoshop CS6
Adobe Photoshop CC
Adobe Photoshop Elements 12
Adobe Photoshop Lightroom 5