Beverly Erlebacher schreef
Government publications departments try to standardize their terms. When
I worked for the Ontario Geological Survey, I saw one of the geologists
in the elevator lobby one day looking exhausted. He had just come out of
a meeting in which an hour and a half had been spent arguing about whether
their publications should standardize on mudcracks, mud-cracks or mud
cracks. The most determined (or obnoxious) committee member tends to get his
way in these situations.

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Seems I have encountered this type of situation :-(

However upon looking further I see that Farrar's Trees in Canada also uses
"redcedar", while the W-Canadian field guide by Brayshaw uses "red-cedar".
The latter is also used in the US book by Grimm, who apparently is trying to
get out from under.
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And then conscientious private publications try to use the "standard"
terms. Meanwhile, ordinary people (and companies selling the lumber and
products made from it) tend to stick to older forms.

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Oddly the following remains a good answer:
The average US-citizen uses "cedar" (when not used as a general category)
for Thuja plicata (western redcedar) and "aromatic cedar" for Juniperus
virginiana (eastern redcedar). The use of "cedar" is connected to the size
of the stands rather than to a particular tree.

Western red cedar is an important commercial species, widely used for
siding and outdoor applications like garden furniture, fences, decks
and utility poles.

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Wester redcedar is big here too. Whenever an architect wants to appear
"modern" he uses this as siding. Although the country by now is full of such
buildings it remains problematic for contractors since the nails all too
often are hammered in wrong.
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I don't know how big the two eastern species get
further south in their ranges, but up here (Ontario) they are small
trees, which make very knotty lumber.

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Eastern redcedar was world famous for its beautiful clear wood which was
sold the world over in pencils (hence its name of "pencil cedar"). It
becomes a medium-sized tree up to 100 feet (30m), but mostly it is academic
since all the worthwhile stands have been cut down methodically.

The rust did not help either.
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White cedar is mostly used for
fence posts and rails, and as a tall hedge or windbreak. A (white)
cedar swamp was once a big asset on a farm. I've only seen eastern red
cedar sold as short narrow boards for panelling closets, and maybe
small chunks for carving and other craft work, which you can hang in
closets or put in drawers to scent your clothes and deter moths.

I think I've only seen the term "aromatic red cedar" used in ads for
the lumber. I don't think I've ever heard it used in reference to the
tree.

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I have never seen "aromatic red cedar" only "aromatic cedar", but indeed
only for the wood.
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Btw, in this climate, (white) cedar fence rails can last a century.

To call Thuja "arbor-vitae" goes back quite some time (perhaps long
enough for Mike Lyle's dictionaries to have captured usage? :^).

I see arborvitae (without the hyphen) used here mostly for cultivars used
as specimen trees or shrubs. The run-of-the-swamp forms are sold as "cedar
hedge" or "hedging cedars" by height, in quantities.

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"arborvitae" is used only for the living tree (this makes sense since the
wood would be lignum vitae, wouldn't it? :^), but there is no clearcut way
of writing. The British and "official US" spelling is one word, but the
"official US" books tend not to use it. The Audubon guides follow this, one
word. However the Peterson's use "Arbor Vitae", which appears to be quite
popular on the internet too. Indeed "arbor-vitae" is a minority point of
view, but can be found.
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In Ontario, white cedar occurs both as dense pure stands in swamps, and
on very dry and shallow soils of abandoned fields. Eastern red cedar
is mostly found in the latter context, but almost exclusively around
the northeastern shores of Lake Ontario. You can see a lot of
virtually pure stands near Kingston where the soils are very shallow
over a Paleozoic limestone plain. Further north, and on the more
acidic soils overlaying Precambrian granites, it's white cedar all the
way.