The American tree is not related to the gums of Australia, Eucalyptus (several species).

It was the "several species" that got me.

When I started as a practising botanist (early 60s in SE Oz) there were at least 450 species (according to the "lumpers" among taxonomists) or as many as 650 species (according to the "splitters", ditto), and that's not counting hybrids or the proliferation of PhD candidates wanting to leave their mark. More recently, the whole genus has been split so that what nonspecialists call "eucalypts" (as the common and garden generic term) is misleading; many are no longer in the genus Eucalyptus.

Enough thread drift. But, at the risk of confusing searchers of the DT, which includes both "Gum tree" and "Gumtree" it is rare in Oz to see the two words conflated into only one when referring to anything arboreal; even the hyphenated version legitimately and properly quoted by Bob would probably, now, be regarded as archaic usage.

Cheers, Rowan