There are three species listed for North America:
American mountain-ash
Sorbus americana
Showy mountain-ash
Sorbus decora
Sitka mountain-ash
Sorbus sitchensis
The first two are Eastern.
According to Farrar's "Trees in Canada"
S. americana
is a shrub or small tree to 10 metres.
There is an isolated population in Pennsylvania, otherwise southern New
York to southern Labrador, Newfoundland west to around Rainy River (and NE
Minnesota).
S. decora
is a small tree to 15 metres.
There are isolated populations in Ohio, Indiana, Wisconsin, Vermont,
otherwise from Georgian Bay to the east end of Lake Ontario, north
almost to Ungava Bay, Newfoundland west to south central Manitoba.
S. sitchensis
is a shrub or shrubby tree to 6 metres
found in B.C. and western Alberta; nothing is said
about the U.S.