from one show to another show (NOT A SPIN-OFF) but the character WAS NOT THE SAME PERSON? The characters name was different, but the characteristics were basically the same? After checking out the posts on the Three's Company movie thread, Suzanne Somers was threatened for trying to use the Chrissy character on another show (CBS) which never aired because of the similarities of the character she was playing. that's what made me wonder if this ever occurred.

I can think of a few good examples, but you're right - often it's a similar character even if the show is completely different (ex: all of Lucille Ball's characters, Bill Daily on "Bob Newhart"/"I Dream of Jeannie", Don Knotts on "Andy Griffith"/"Three's Company") - but here is where I can see some major differences:

Larry Hagman on I Dream of Jeannie and Dallas
Ted Danson on Cheers and Becker