You're info is a bit wrong.
Jerry and Nelson are not too different people. The man's name is Jerry Nelson. He originaly p[ayed Statler in the Muppet Show Sex and Violence pilot. When season 1 of The Muppet Show came along, Jerry was busy for many epsiodes so the role was taken over by Richard Hunt who crated the Statler we all know and love. Sadly, on January 7, 1992 Richard Hunt passed away. Jerry Nelson then came in and took over once more. Once Jerry decided to retire from all things Muppet (but not Sesame Street) the role was passed between Steve and Bill, but Steve won out and is now the one who performs Statler. He is the one that performed Statler on AFV and MWoO and will likely continue for many years to come.