There are three parts to "Apple Remote Desktop"
1. The 'server' side - this is what each machine runs that allows OTHER machines to reach in and control it. This is built in to OS X. This is in System Preferences, under Sharing. You can have it share with the stock Apple Remote Desktop protocol, or with the open VNC protocol (which requires an extra step to enable because Apple doesn't support the secure version.)
2. The 'simple client' side - this is what you run on a remote machine to connect to machine #1 - OS X comes with it built-in, but it's hidden by default. It is an app called simply "Screen Sharing.app" in /System/Library/Core Services/Applications (in Yosemite - in earlier versions it's in just /System/Library/Core Services.) I make an alias to it in my main Applications folder. This client can connect to machines running either the Remote Desktop or VNC protocols. (In fact, from Safari, you can launch it directly by using a URL such as vnc://servername ) This is also the app that is launched if you use the network browser in the OS X Finder to see a system on the local network, and click "Share Screen" on it.
3. The 'complex management' software - this is the $80 package. This allows for not just viewing and controlling the desktop remotely, but for easy management of many machines remotely, including pushing out software packages (want to install Pixelmator on 10 systems at once? You can with this.) It allows you to view thumbnails of many systems screens simultaneously. It allows you to remotely connect, and lock the local screen and keyboard! (Useful if you run a computer lab, and need to change a setting and you don't want the local user to see what you're doing - they will see a gray screen with "this computer is being controlled remotely" or some similar message.)
For home, and even very small business/education environments, the built in components in #1 and 2 above are probably fine. #3, the paid software, is for larger/more complex management scenarios, like computer labs or corporate computer management.