A couple of years back, I ran across this picture of (left to right) Herbert, Julius, Leonard, Milton and Adolph Marx. Five brothers who look very much alike! Heck, they could be twins. Well, except for the height difference.
And here is a good lesson in adaptability.
Although the palates are very much alike, add in different make-up, wigs, costume pieces, etc. and you have completely different characters that bear little resemblance to each other:
Project Puppet for an example of this in action. Or how about this old favorite:
... which just goes to show that what makes a character a character is the individual artist's touch; the whimsey that an artist brings to the table.
UPDATE: To illustrate my point further, take a gander at this pic that I swiped from www.puppet-planet.com:
Here you can see the Fraggles at different stages in their construction. Same basic frame, a glorious multitude of possibilities!