There's almost more differences than there are similarities, so allow me to flip it on its head. I will tell you in what ways they are similar:
You can use both to write Swift code.
That's it.
Xcode is a fully blown IDE for development for Apple platforms. It has feature rich tools not just for code editing, but for debugging, testing and asset wrangling. It also works with Objective-C, C++, C and Storyboard based systems with Storyboards editing.
Playgrounds is more of an experimentation and learning environment. Mostly for new programmers but also for experienced ones who want to try out a quick idea without firing up the heavy Xcode.
While the ability to submit apps to the App Store from Swift Playgrounds on iPad was introduced it is still not really a proper development environment and it really doesn't scale beyond tiny simple apps.
Xcode also has a section called Playgrounds within Xcode intended for experimentation. This is distinct and separate from the Swift Playgrounds app, but conceptually similar in that it's an environment for quicker experimentation.
If you're new, Playgrounds has some decent learning material but aside from that it's not that serious a tool