Actually, you have joules defined wrong.
Here are the correct versions in fundamental units:
1 Joule = 1 kg-m^2/sec^2
1 Newton = 1 kg-m/s^2
The difference, or better spoken as the "quotient", between Joules and Newtons is meters. This is because Joules measure work and energy, and Newtons measure force.
Work is the cumulative effect of the aligned component of force applied over a distance.
Formally it is defined as:
W = ∫F·dx
where F is a force vector at a given instant, and dx is an infinitesimal change in position as a vector at that instant. Carry out the line integral and you have the work. The dot product produces only the aligned component of force and distance.
In a more simplistic case of a constant force always aligned with the motion, work is a simple product:
W = F*x
Now you see why "meters" is the quotient between Joules and Newtons. Newtons measure force, and when you apply that force through a distance, you do mechanical work. Joules also measure energy, any type of energy, which is the result of doing mechanical work.
So Joules are Newton-meters...
Isn't torque also measured in Newton-meters?
Yes, however when the quantity is as simple as energy and isn't a vector, we name the unit the Joule. When the quantity is torque, the rotational twisting force, we preserve the Newton-meters to remind ourselves that it is still a vector. 1 N-m of torque doesn't become 1 Joule of work until it is applied while the target rotates 1 radian.