I don't get it :-(

I think it's just that Andrew Carnegie made his fortune in the steel industry, and the Mellons made their fortune in banking.

Yes and

Carnegie Technical Schools was founded in 1900 based on a $1m donation from Andrew Carnegie,

Mellon Institute of Industrial Research was originally founded in 1913 by Andrew and Richard Mellon.

Carnegie Mellon was created by combining the two institutions in 1967.