The OED defines "democratical" to mean the same thing as "democratic," and it gives some usage examples going back to 1589 and continuing only to 1850:
1589 ‘M. Marprelate’ Hay any Worke for Cooper 26 It is Monarchicall, in regarde of our head Christ, Aristocraticall in the Eldership, and Democraticall in the people.There are also a 3 examples of "democratical" as a noun, defined to mean the same thing as "democrat." 2 of these are by Thomas Hobbes:
1608 D. Tuvil Ess. Polit. & Morall f. 4v, Ostracismes practiced in those Democraticall and Popular states of elder times.
1686 in Coll. Scarce & Valuable Tracts (1748) I. 111 The Democratical Man, that is never quiet under any Government.
1791 J. Boswell Life Johnson anno 1775 I. 460, I abhor his Whiggish democratical notions and propensities.
1850 G. Grote Hist. Greece VIII. ii. lxiv. 231 The levy was in fact as democratical and as equalising as..on that memorable occasion.
1651 T. Hobbes Leviathan ii. xxii. 122 Aristocraticalls and Democraticalls of old time in Greece.What, you may ask, is the "-al" ending doing after the "-ic" ending? When do suffixes double up like that? This seems related to the present-day controversy about using the word "Democrat" as an adjective, when GOP types refer to the "Democrat Party," instead of the "Democratic Party." There's an insult perceived in leaving off the "-ic" ending, but, oddly, in the case of "democratical," there's insult in adding more letters — "-ic" plus "-al."
1679 T. Hobbes Behemoth i, in Wks. VI. 199 The thing which those democraticals chiefly then aimed at, was to force the King to call a parliament.
Does "-al" have any meaning? "Forming adjectives with the sense ‘of or relating to that which is denoted by the first element'" is the OED definition, which seems to say, it's just a way to turn something into an adjective. But that doesn't explain "-ical." The "-ic" already made the adjective. What's up with "-ical"? What are the other "-ical" words? Comical, radical... logical...
I know what you're thinking: "The Logic Song" by Supertramp!
When I was young, it seemed that life was so wonderful, a miracle, it was beautiful, magicalAm I thinking too logical? So... musical interlude over. What does "-ic" mean? It's just another ending used to make an adjective and means "in the manner of" or "pertaining to" or some such generic way to say what differentiates an adjective from a noun. So what's with the suffix pile-up in the "-ical" words? Wonderfully, magically, the OED has an entry for "-ical":
And all the birds in the trees, well they'd be singing so happily, joyfully, playfully, watching me
But then they send me away to teach me how to be sensible, logical, responsible, practical
And they showed me a world where I could be so dependable, clinical, intellectual, cynical...
I said now, watch what you say, now we're calling you a radical, a liberal, fanatical, criminal
Won't you sign up your name, we'd like to feel you're acceptable, respectable, presentable, a vegetable...
But I'm thinking so logical ...
Sometimes forming an adjective from a noun in -ic, as music, musical, but more frequently a secondary adjective, as comic, comical, historic, historical. Its origin appears to have been the formation in late Latin of adjectives in -ālis on nouns in -ic-us, or in -icē, e.g. grammatic-us grammarian, grammaticē grammar, grammatic~āl-is grammatical, clēricus clergyman, clerk, clēricāl-is clerical. So in medieval Latin, chīrurgicāl-is, dominic-āl-is, medicāl-is, mūsicāl-is, physicāl-is. In French, adjectives of this type are few, and mostly taken directly from Latin formations, as chirurgical, clérical, grammatical, médical, etc. But in English they are exceedingly numerous, existing not only in all cases in which the term in -ic is a noun, but also as the direct representatives of Latin adjectives in -icus, French -ique. Thus we find before 1500 canonical, chirurgical, domestical, musical, philosophical, physical. Many adjectives have a form both in -ic and -ical, and in such cases that in -ical is usually the earlier and that more used. Often also the form in -ic is restricted to the sense ‘of’ or ‘of the nature of’ the subject in question, while that in -ical has wider or more transferred senses, including that of ‘practically connected’ or ‘dealing with’ the subject. Cf. ‘economic science’, ‘an economical wife’, ‘prophetic words’, ‘prophetical studies’, ‘a comic song’, ‘a comical incident’, ‘the tragic muse’, ‘his tragical fate’. A historic book is one mentioned or famous in history, a historical treatise contains or deals with history. But in many cases this distinction is, from the nature of the subject, difficult to maintain, or entirely inappreciable.That's long and complicated, though interesting as hell, but I boldfaced the bit that's most useful to understand what John Adams and Thomas Hobbes were getting at. It might be helpful to consider what it would mean to say: This political movement is not democratic. It's democratical. My sense is that democratic would refer to the principle that each person to be governed ought to vote. Democratical nudges us to worry about the chaos and disorder of attempting to let everyone decide everything.
Adjectives of locality, nationality, and language, as Baltic, Arabic, Teutonic, and those of chemical and other technical nomenclature, as oxalic, ferric, pelagic, dactylic, hypnotic, megalithic, have usually no secondary form in -al.
This brings us back to why Democrats prefer the adjective "Democratic" (rather than to have the noun "Democrat" used in the combination "Democratic Party"). Presumably, they want to appear to be imbued with democratic values, rather than simply to be a party composed of Democrats.
A "Democrat" is, in the U.S. political sense, "A member of the Democratic party," as defined in the OED, beginning with this choice 1798 quote from none other than George Washington: "You could as soon scrub the blackamore white as change the principle of a profest Democrat."
There are times when all the world's asleep/The questions run too deep for such a simple man...