Acacia is the genus name of the acacia tree. But that's only part of the scientific name. It needs to be followed by the specific species name. For example, Acacia plicata is the wattle tree of Geraldton and Perth in western Australia. Acacia implex is the Australian acacia or Lightwood tree. Acacia heterophylla is the Highland tamarin or Tamarin des Hauts of La Réunion, an island quite a bit off the coasts of Madagascar.

Thalia dealbata was created in 1820.

Cyathea dealbata was created in 1786.

The word "mimosa" has been applied to several different trees. One of them is the Silver Wattle tree (Acacia dealbata), another is the Cootamunda Wattle tree (Acacia baileyana), and yet another is the Silk tree (Albizia julibrissin). Also, a number of other trees in the genus Acacia have been called "mimosa". If that wasn't already confusing enough, Mimosa is a genus in its own right, with several hundred species.
Mimosa pigra

Cyathea dealbata