Yes. The UDK is related to UE4 - The UDK is based off of Unreal Engine 3 to which Unreal Engine 4 is the successor.
To the initial end user a number of things have changed. Unreal Engine 4 replaces UDK's Kismet Visual Scripting system with Blueprints. You can do practically everything with Blueprints and in some ways Blueprints can be considered a replacement for UnrealScript.
UnrealScript is also gone. Instead of this you would now use Blueprints, or C++. Unrealscript is object-oriented and had some similarities with C++ and Java syntax, so while a lot has changed using C++ won't be too unfamiliar with someone who is well versed in UDK.
The interface has changed, things have moved around and what not - all of this will take some time but thanks to the comprehensive documentation it shouldn't be to difficult to figure out what is what.
One of the biggest changes, is that with UE4 all of the engine's source code is made available to you. For most users this won't matter, but for those that it does matter to - this is a very good thing. To gain access to the Unreal Engine 3 source as a UDK user - you had to license UE3.
The running suggestion has been, if your game is currently near completion in UDK then stick with UDK. Otherwise it's worth it to check out UE4. UDK projects will not open in UE4 - and you'll have quite a bit of work porting things over (as the scripting system, and visual scripting have all been replaced). That said Epic does provide a handy Transition Guide for people leaving UE3 (and UDK) for UE4.