A few days ago I hurriedly typed adaption rather than adaptation. Adaption isn’t wrong – it’s in multiple dictionaries and Pages for Mac accepts it – it’s just far less common than adaptation.
Starting with adapt and adopt, there’s no particular reason why adaptation and adoption are standard, adaption is rare and adoptation is either very rare or wrong (Pages for Mac auto-corrects it to adaptation, then red-underlines it when I change it back.) Perhaps it’s related to the fact that opt by itself is a verb, whereas apt is an adjective. But that shouldn’t matter as long as adapt and adopt are both verbs.
Humans tend to want to say things as economically as possible. Adaptation and adoption are standard, so English speakers are more likely to shorten adaptation to adaption than to lengthen adoption to adoptation.
This got me thinking about the whole process of derivational suffixes in English. Humans will say longer word if there’s a change in meaning or word class. Adapt and adopt aren’t good examples, whereas act gives far more examples:
act (verb, noun) > active (adj) > activate (verb) > activation (noun)
act (verb, noun) > activity (noun) > do an activity (verb phrase)
act (verb, noun) > action (noun) > %action, %actionis/ze (verb) > %actionis/zation (noun)
(among others)
Some people complain about or reject either or both of zero derivation (action as a verb) and overuse of –is/ze (actionis/ze) (partly because these are associated with business-speak), but these words fill a useful gap. Actioning or actionising a request or order isn’t the same as activating it, or even acting on it. The client makes or submits a request or order and the service worker ____s it. Google Ngrams suggests only receives, grants or refuses, which is not what we’re looking for. Fulfil is possible, but that means completing the action. Is the service worker the actioner? (Not auctioneer, which Pages for Mac just changed it to.)
See acclimate v acclimatise and direct for similar thoughts.
Never Pure and Rarely Simple 
“adopt” -> “adoption” for the same reason that “opt” -> “option”. The root is the Latin verb “optare” (to choose). The -tion suffix is generally based on the Latin past participial form, which would presumably be “optatus.” Why the -tion form of “option” isn’t “optation” I have no idea, but that’s what you need to find out. Normally, “are” verbs have “ation” nominal forms (so “adapt” -> “adaptation” is the normal expected form).
“act” is from the past participial form of Latin “agere” (as in “agent”), I guess “actus”, hence “action” and its other derivatives. (I would be more precise if I had access to a Latin conjugator.)
In my childhood I read a section of the Golden Book Encyclopedia titled “Adaptation to Environment” and remember recalling it as “Adaption to Environment.” Unless that’s what it actually said.
Also, not to cast aspersions (or aspirations, as a former rock star was quoted as saying recently) on non-American spelling, but “fulfil” for “fulfill” just strikes me as overzealous reduction of letter doubling.
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I originally included *aption/option as another example, then deleted it. Many of these issues in English actually trace to Latin -are, -ere and -ire verbs endings, and also to whether the English word is derived from the infinitive or the past participle (eg agent and actor are ‘the same word’).
I would naturally use fulfill, I can’t remember whether I typed that and Pages changed it or whether I changed my spelling mid-typing. WordPress is now red-underlining fulfill. Google Ngrams shows fulfil is strongly BrEng, while AmEng changed from fulfil to fulfill in the late 1800s.
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