From an American culinary perspective, while generally "sultana" and "raisin" are interchangeable, the unqualified sultana is a light-colored fruit and the unqualified raisin is a dark-colored fruit.
To rewrite this recipe using typical American English, replace "sultanas" with "golden raisins."
I would expect the recipe would be as easily understood in the UK if "raisins" were replaced by "dark sultanas;" however, this is contested in the comments below.
The issue of seeds is not relevant, as the vast majority of raisins are produced from the Thompson Seedless grape, including those known as sultanas. From Raisin Grape Varieties:
‘Thompson Seedless’ [grapes are] dominant in most commercial
raisin-producing countries worldwide.
However, the nomenclature issue is less clear-cut than I originally thought; the same book has this to say about the Thompson Seedless grape (emphasis mine):
The variety’s most widely accepted name in the literature is
‘Sultanina,’ a derivation of ‘Sultanieh,’ believed by some to be a
recognition of a sultan’s appreciation for or ownership of the grape,
or of its possible origination in or near the town Soultanieh, which
is situated in Persia not far from the Caspian Sea. Other synonyms are
‘Oval Kechmish’ (Iran, Persia), ‘Kouforrogo’ (Greece), ‘Tchekirdeksiz’
(Turkey), and “Sultana” (Australia and South Africa).
There is another grape described near the end of the chapter as a "misnamed variety:"
The earliest introduction (mid-1800s) of this misnamed variety was by
a Mr. West, a Stockton nurseryman. It was distributed as “Sultana”
under the mistaken impression that it was the variety from which the
‘Sultana’ raisins of commerce were produced. Colonel Agoston Haraszthy
also imported the same variety from Spain in 1861. It probably was
introduced into Europe from Asia Minor. It is described under the name
‘Round Kishmish’ in French ampelographies, and should not be confused
with the true ‘Sultanina’ (Sultana) that we know as ‘Thompson
Note that while this text addresses the origin of the name Sultanina, given to the grape variety I've been calling Thompson Seedless, it doesn't directly address the origin of the name Sultana, given to the dried fruit produced from that grape (and to an ostensibly unrelated grape variety).