Where is the OS X Remote Desktop Client

Solution 1:

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]

Solution 2:

Perhaps you’re referring to the Screen Sharing app. It’s in Macintosh HD > System > Library > CoreServices.

P.S. You don’t need to launch this app directly to connect to another computer via VNC. You can just go to Finder > Go > Connect to Server… (or press ⌘K) and enter vnc:// and the address of the remote computer. This app is also used by the Back To My Mac screen-sharing feature.

Solution 3:

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

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