"Species" is the Latin name that follows the genus name. It is sometimes
followed by a subspecies name or a variant name or both. For example:

Rhododendron calostrotum ssp calostrotum var gigha
is a shrub noticeably different from the even tinier
Rhododendron calostrotum ssp keleticum

A variant or a subspecies is a naturally-occurring plant, not a cultivar,
though clones & cultivated strains are sometimes given names as though
they were cultivars even if they're not. The little rhody above named is
sometimes called "Gigha" capitalized & in quotes, as though this were a
cultivar name, though it is in reality a variant name & not a cultivar --
a variant name is neither capitalized nor in quotes, but by common usage
it has become its common name in commerce.

If one followed protocol exactly, names like Rhododendron "Gigha" or
Rhododendron "Milestone" would not have these names in quotes, because the
quotes indicate a REGISTERED cultivar. "Gigha" being a natural variant, &
"Milestone" beng an UNregistered cultivar ought to be given as Gigha or
Milestone, or else following the Genus name placed between parentheses, as
Rhododendron (Gigha) or Rhododendron (Milestone).

But the niceties of these specifics are rarely followed by us mere
gardeners, & really virtually never followed even by retail nurseries. The
Hoop petticoat narcissus sold as "Golden Bells" is nearly always placed in
quote though this is incorrect; & many are the claims in catalogs that it
is an improved cultivar of the botanical daffodil (one catalog claimed it
was the culmination of 20 years of hybridization -- it is not). In reality
the registrar refused to register it, because it was not distinct from the
regular botanical species. So "Golden Bells" is either an illusion trumped
up by a Dutch grower in order to sell more bulbs, or at best a selected
strain (possibly more floriferous than the species as a whole), & the name
of which should be given as Golden Bells or as Narcissus bulbicodium
(Golden Bells), but not in quotes.

A common name like Coneflower or Dandylion is also never rightly given in
quotes. The majority of true botanical tulips seem to have no common names
beyond Wild Tulip or Botanical Tulip, but when there are exceptions, such
as for Tulipa kolpakowskiana sometimes called Soltulipen or Sun tulip; or
Tulipa clusiana often called Lady tulips or Candlestick tulips, these
names would never be in quotes. (I can dream up exceptions, like: My
grandmother always called Lady Tulips "Candlestick Tulips." )

Further, Latin names (genus, species, subspecies, variant or forma) are
given in Italics, but common names, cultivar names, or named select
strains that are not cultivars, are not given in italics. When
abbreviations like var. or ssp. are inserted (& they are optional) these
should not be in italics, only the Latin part is italics. But again, the
specific niceties are ignored by most of us yobs, though important for
anyone seeking to be taxonomically precise.

But even people who probably know better don't follow these rules exactly
because it can make for a text-presentation that looks like it lacks
uniformity, when read by hobbyists rather than taxonomists.Some gardening
magazines have their in-house styles that ignore some of the lesser rules
for the sake of their own type-design uniformity. When not trying to be a
scientist about it, it's okay to ignore the minute details of the
protocol. For us amateurs, Latin names are in italics, named varieties
whether or not cultivars are in quotes capitalized but not in italics, &
common names are neither in quotes nor italics, capitalization optional
since taxonomic & registration rules don't address official regulations
for common names.

At my website I put in italics any word or phrase or name that is a "hot"
link to another page, & this means many exceptions to taxonomic rules when
a Latin name followed by cultivar name is a link-term hence entirely in
italics (& in a different typeface color to make it totally clear it is a
link). About once every two months someone sends me an e-mail because it
annoys them that cultivar names sometimes appear in italics. But it annoys
even more people that I use ambersands instead of the word "and." All
grundiesque complaints are to be ignored.

-paggers

--
"Of what are you afraid, my child?" inquired the kindly teacher.
"Oh, sir! The flowers, they are wild," replied the timid creature.
-from Peter Newell's "Wild Flowers"
See the Garden of Paghat the Ratgirl: http://www.paghat.com/