Adobe has always had a professional (Pro) and basic (Reader) version of their Acrobat software. In fact, on Windows, there are three versions with a Standard and a Pro version. Mac users used to have a standard version back in the day too, but that option is no more. Then there's the naming scheme for the basic (Reader) which has changed over time including "Acrobat Reader", "Adobe Acrobat Reader", "Adobe Reader" and now "Adobe Acrobat Reader DC" or "Adobe Acrobat Reader 2015".
With the launch of Adobe Document Cloud in 2015, comes more versions of Acrobat, even more confusing than before. There's a "classic track" and a "continuous track" - it would appear that the classic track is the non-Cloud/subscription (2015) version and DC is the cloud/subscription (DC - Document Connect) version but this is not clear at all. On the Mac each of these track versions are available in a Reader and a Pro version. At least the Pro version is available to buy separately outside of the extortion racket of their subscription Cloud service. Adobe outlines the differences between the subscription and non-subscription versions here with the DC version's features highlighted as "Subscription only".
Okay, so basically if you don't want to sign up forever to Creative/Document Cloud (and hope Adobe don't ever change/cancel your subscription) you can buy Acrobat Pro "classic track" version as a standalone product. But when you get this product, it confusingly comes in an Adobe Acrobat Pro "DC" box. When you install it, you must sign in using your Adobe ID - that's fair enough as this started back with Creative Suite CS6 and it registers your software with Adobe but now, you have to stay signed in even if you wanted and bought the "classic track" non-Document Cloud/subscription version. If you sign out it deactivates your software. You didn't buy the Document Cloud version, yet you get a DC box and software that requires you to be signed in and has options all over the place for the "Document Cloud" e.g. Storage area, Mobile Link and Preferences synchronisation!
If you want to download the basic Reader version at https://get.adobe.com/reader it only offers you the DC version! If you want the classic track version you must download it manually from their FTP site.
Adobe dropped support i.e. no more security updates for Acrobat X on 15th November 2015. They gave users a subtle reminder for this in an obscure blog post on 14th September 2015. If you are still using Acrobat Pro X I recommend you take action to stay secure. This is especially important for the many people who are holding out on Adobe Creative Suite CS6 as that came with Acrobat X. Unfortunately the only option is to upgrade Acrobat Pro and Adobe offers no upgrade path for Creative Suite users so you're looking at an out-an-out purchase at full price and then dealing with what updating it as outlined in this blog post!
After you've dealt with all the above versions and naming conventions you now need to keep your Acrobat software up-to-date and you definitely want to do that as it's Adobe software (full of security holes) and naughty PDF files are a primary attack vector. Adobe has information on updating Acrobat along with various technical details here but by god, it's very poorly written and quite difficult to follow.
In older versions of Acrobat Pro/Reader in the preferences you had several options for installing updates:
However, in the new 2015/DC version of Acrobat updating is considerably different. You have no control over updates with the Reader version at all which will update automatically (you hope). Then there's the Pro version which now only has one option in the Preferences:
The aforementioned help URL/link tries to explain the update scenarios/options but basically Mac users get shafted with little, or no choice/control and the way it currently works appears to be par for the course with Adobe - i.e. bloody awful. It does strike me, once again, how bad Adobe is at designing and writing software for end users and also for treating Mac users like second class citizens.