It is written differently in its radical form indeed, as it often happens with radicals.
Another website showing decompositions is Wiktionary, e.g.: https://en.wiktionary.org/wiki/%E7%88%AB
According to Wiktionary, in Mainland China, Hong Kong, Taiwan and Vietnam (see the GHTV mark):
爫 = ⿱丿⺍
⺍ = ⿲丶丶丿
=> 爫 = ⿱丿⿲丶丶丿
While in Japan and Korea (JK for Japan and Korea):
爫 = ⿱丿⿲丿丶丶
So, depending on the country,
爫 is either 丿丶丶丿 (in GHTV)
or 丿丿丶丶 (in JK).
This is unfortunately normal situation: stroke order differs not only between radical and standalone forms but also from country to country.
In English there are differences in spelling, too, e.g.: threater vs. theatre.
Update on 爫 = ⿱丿⺍
Wiktionary does say this, but the character is not displayed correctly due to browser-unicode-font limitations. See the screenshot: