Represent the sides of the triangle.

Let the sides of the triangle be $x$, $2x$, and $3x$, since they are in the ratio 1:2:3.

The perimeter of a triangle is the sum of its sides.

The shortest side is $x = 9$ cm.
The longest side is $3x = 3 \times 9 = 27$ cm.

Difference = Longest side - Shortest side
Difference = $27 \text{ cm} - 9 \text{ cm}$
Difference = $18 \text{ cm}$

The correct option is C.
The difference between the shortest and the longest side is $\boxed{\text{C. } \text{18cm}}$.