UDK was what they called the SDK for Unreal Engine 3.
Unreal Engine 4 doesn't use the UDK name anymore, likely because it's not just an SDK that is available for most-people anymore, it's the entire engine.
My question is, is UDK and UE4 similar with UE4 being improved, and can I watch UDK videos and apply on UE4?
UE4 is a pretty significant change from UDK/UE3. Some aspects and concepts from UDK may be applicable, but you are probably better off using UE4 resources to get started. Epic has and continues to release a substantial amount of resource through their website, and their YouTube channel. There is also loads of 3rd-party resources out there.