Sesame Street used completely different types of muppets (except for Kermit) than on The Muppet Show. Sesame Street relied on "Anything Muppets" while The Muppet Show relied on "whatnots". I wonder if even monsters on Sesame Street (including Cookie Monster) were actually Anything Muppets wearing what appears to be colored shag fur? But then again, maybe Sam the American Eagle's likeness may have been somewhat inspired by Beautiful Day Monster - since the latter first appeared in 1969, while Sam didn't debut until as early as 1976.
But I don't see any comparison, since Sam is light blue, and BDM was actually a darker blue. But were both muppets voiced by the same voice actor? Frank Oz did voice Sam, according to Muppet Wiki.
Also, I learned that Beautiful Day Monster did appear on The Muppet Show at some point. Were he and Kermit, the only Sesame Street characters to appear on more than one episode of The Muppet Show? (Big Bird, Bert and Ernie doesn't count, as they were guest stars)
I also learned that BDM later appeared on The Cosby Show at one point (he was then voiced by Elmo's voice actor, Kevin Clash). He even appeared in the movie Muppets Most Wanted, and that was released in 2014.