What the difference between background-color and background in css3 ?

Answer 1

background is shorthand
background-color is more specific

Further reading:

https://www.w3schools.com/cssref/css3_pr_background.asp

Answer 2

the "background" keyword allows you to set any background you want (images etc) while the "background-color" allows you to set only color backgrounds.
Their connection is like class-class.property