You can say it all you want, but a Joule is J=m*d^2/t^2, while Ek=1/2m*d^2/t^2 and is in Joules. I honestly just used the former when I shouldn't have, as while I know offhand what a Joule is, I didn't remember the constant for Ek.
It's pretty much exactly like how surface area is in m^2, but the surface area calculation for a right angle triangle is ab/2, but is still referred to in the unit metres squared. If you just did ab, you'd end up with metres squared, but you're doing it for a square, not a triangle.