From a user perspective the difference is important, because it's often the difference between "can use this for real work without worrying about exactly what's going on under the hood" and "you probably shouldn't use this unless you know you need to use it and that you can live with the performance aspects". (e.g.: booting a Windows guest under virtualization is a very popular thing to do; booting a Windows guest under emulation is probably going to be a lot of work and not actually achieve the end-goal you were after when you do eventually get it running.) They are also vastly different from a technical perspective.
They are very important distinctions and they are completely different.
Virtualization abstracts the actual underlying hardware, creating a virtual instance. You are executing instructions directly on the host CPU with little or no overhead, so it’s fast.
Emulation mimics one system on a different system by converting the instructions of the mimicked system into instructions the host platform can understand. It is generally a very slow process.