What is the difference between Big O and asymptotic notation?
Bachmann–Landau notation or asymptotic notation is collection of notations one of which is Big-$O$. So they are not interchangeable, because as asymptotic notation also is known little-$o$, big-$\Omega$, big-$\Theta$ etc.
Historically this symbol was introduced by German  mathematician Paul Bachmann and then adopted by German number  theoretician  Edmund Landau and American mathematician L.E. Dickson . Big-$O$ was shorthand for function rate of growth, which is called its order.
History also can be viewed in the book by Florian Cajori - A history of mathematical notations-Dover Publications (1993), page 31.