Is it "flotation" or "floatation"?
I'd have to say that the difference was influenced by something else.
According to the Online Etymology Dictionary, the French influenced the more widely used spelling flotation.
And according to the same root-source regarding floatation:
the older, more etymological, but less popular spelling of flotation
Several of these sources (will list below) all agree that floatation and flotation are variant spellings of one another.
M.Webster
Collins Dictionary
And (my new favorite word coming up) according to this source, there is no specific difference between BE and AmE regarding to flotation/floatation confusion. I'd like to point out, his site has similar sources to back up his findings.
I wasn’t aware of the floatation spelling, or that it was found in American English. The OED has only flotation, but with this note:
The spelling flotation is not etymologically justifiable, but is more common in use, probably because it disguises the hybrid formation, so that the word appears more conformable to the general analogy of scientific terms.
Summary: It's Scots, laddie.
I am a British Empire Antipodean, but well versed in the mother tongue, and long in the tooth to boot, but until now had never encountered "floatation" as a word.
Google NGrams show as below, with "floatation" appearing at about 1800.
Further searching produced a result which surprised me. It's Scots, laddie. The term "floatation" is widely used in Scotland, as opposed to the UK in general, being much more common than "flotation". While this can be confirmed by searching the web for floatation and reading Scottish related entries, a good idea of what will be found is obtained by searching the web for
"floatation" related_term
flotation related_term
The quote marks around the 1st term tend to make at least Google offer fewer entries with suggested alternatives.
Some results for floatation and flotation with various related_terms are below. M = millions of hits. k = 1000's of hits.
e.g. "Australia 420 k / 10.9 M" = 420,000 hits for floatation and Australia, 2.29 million hits for Australia and flotation.
Very obviously this method has methodological deficiencies, but it is also demonstrably useful.
floatation / flotation.
All 3.69M / 10.9M
Australia 420 k / 2.29 M
England 266k / 2.23M
Scotland 2.01 M / 445 k
USA 689 k / 3.52 M
Scottish 2.38 M / 261 K
Scots 2.327 M / 659 k
NZ 252 k / 1.18 M
"South Africa" 181k / 994 k
Wales 117 k / 341 k
"pinyin" 37k / 206 k
fwiw
"English" 600 k / 1.92 M
ie adding the quotes around "English" did not greatly affect the result.
One could go on :-).
But the two Scots related entries are about 4:1 and 9:1 in favour of floatation.
All others and overall result are strongly biased towards flotation.
An examination of some of the Scots related pages shows widespread use of "floatation" in contexts that would be foreign to most people reading this posting.
BUT:
Russian 2.84 M / 864 k - A Scottish translator writer is suspected :-)