There aren't actually single nation-wide standards about how to hyphenate words. The tool is just based on two specific conventions that are common, but not universal in their respective countries. There are various principles about how to hyphenate words, and by assigning different relative weights to these principles, many different specific hyphenation patterns may be derived.
The "British English" hyphenation on that web site is apparently based on a list provided by the Oxford University Press. It seems to use more morphological or etymological hyphenation: the word "editorial" is hyphenated in a way that corresponds to the end of the words "edit" and "editor".
The US hyphenation is apparently based on the "Plain TeX hyphenation tables", which in turn seem to have been based on Webster's Dictionary. It seems to use more phonological hyphenation: the word "editorial" is hyphenated in a way that doesn't break apart the stressed syllable "to", and the "r" is put in the onset of the following syllable in accordance with the widely recognized principle of "maximizing onsets" in syllabification whenever possible. (Webster would have syllabified the "d" of "editorial" with the first syllable because of the preceding short vowel sound, but traditionally, the "o" in "editorial" was a long vowel.)
I don't know the motivations behind the hyphenations in Webster's Dictionary, but the use of more pronunciation-based hyphenation might be related to Noah Webster's preference for basing spelling on pronunciation rather than on etymology (when possible).