Where is the OS X Remote Desktop Client

"To take advantage of the functionality you've just seen updated, you probably need ""Apple Remote Desktop"", which seems to be an enterprise remote management tool like Microsoft's Systems Management Server, but for OSX.

The update you're referring to probably updated unseen client-side support built into OS X. For desktops that aren't being managed by Apple Remote Desktop, I would guess the update is innocuous.

UPDATE: For what it's worth, I just ran Software Update on my own MacBook and saw the update you're referring to. Here's the link to Apple Support's article describing the update. In fact, it mentions:

[...] Apple Remote Desktop Client 3.3.1
updates the software that facilitates
Remote Management (enabled in Sharing
preferences, in System Preferences). [...]
[emphasis mine]"

"On Yosemite, you'll want to use the Screen Sharing application. You'll find it here:

/System/Library/CoreServices/Applications/Screen Sharing.app"

"Cross-post from AskDifferent for Googlers

If you are trying to access one of your own computers that uses your same Apple ID, the best method is to use Back to My Mac.

You have to make sure you enable ""Back to My Mac"" in the iCloud Preference Pane on both computers:

Under the Sharing Preferences pane disable Remote Management if it is enabled, and then enable Screen Sharing.

Wait a moment and your computer should show up in Finder under the Shared section.

If you don't see a ""Shared"" section or the computer doesn't appear there, click on Finder and then open Finder's preferences (⌘+,) and make sure that everything in the Shared section is selected:"