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Are the two interchangeable or is there a difference?

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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.

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