Diameter is a straight line passing from side to side through the center of the figure while radius is the distance from the center of the circle to it's circumference, it is also the half of the diameter.
The diameter is the greatest measurement from side to side [of a circle], the radius is the measurement from the centre to the edge [circumference]. 

The diameter is twice the radius. 

It's worth noting that, though the terms are commonly understood to apply to circles, they may not. One can speak of the largest and smallest diameters of an ellipse or an irregular body such as an asteroid. Radius may also be used to describe an arc of a circle or even may apply to a curve at a particular point (one can calculate the radius of a curve at a point on the curve, for example