1590s, "capable of being distinguished from something else;" see distinguish + -able. Meaning "capable of being perceived" is from 1610s. Related: Distinguishably.
Entries linking to distinguishable
distinguish v.
1560s, "recognize as different or distinct from what is contiguous or similar; perceive, make out," from French distinguiss-, stem of distinguer, or directly from Latin distinguere "to separate between, keep separate, mark off, distinguish," perhaps literally "separate by pricking," from assimilated form of dis- "apart" (see dis-) + -stinguere "to prick" (compare extinguish and Latin instinguere "to incite, impel").
Watkins says "semantic transmission obscure;" the sense might be from "pricking out" as the old way to make punctuation in parchment or some literal image, but de Vaan derives the second element from a different PIE root meaning "to push, thrust":
The meanings of ex- and restinguere 'to extinguish' and distinguere seem quite distinct, but can be understood if the root meant 'to press' or 'push': ex-stinguere 'to put a fire out', re-stinguere 'to push back, suppress', and dis-stinguere 'to push apart [thence] distinguish, mark off ....
The suffix -ish is due to the influence of many verbs in which it is the equivalent of Old French -iss-, ultimately from Latin inchoative suffix -iscere (this is also the case in extinguish, admonish, and astonish).
Sense of "to mark or note in a way to indicate difference" is from 1570s; that of "separate from others by some mark of honor or preferment" is from c. 1600. Intransitive meaning "make a distinction, find or show difference (between)" is from 1610s. Related: Distinguishing. The Middle English form of the verb was distinguen (mid-14c.).
-able
common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro-, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).
A living element in English, used in new formations from either Latin or native words (readable, bearable) and also with nouns (objectionable, peaceable). Sometimes with an active signification (suitable, capable), sometimes of neutral signification (durable, conformable). It has become very elastic in meaning, as in a reliable witness, a playable foul ball, perishable goods. A 17c. writer has cadaverable "mortal."
To take a single example in detail, no-one but a competent philologist can tell whether reasonable comes from the verb or the noun reason, nor whether its original sense was that can be reasoned out, or that can reason, or that can be reasoned with, or that has reason, or that listens to reason, or that is consistent with reason; the ordinary man knows only that it can now mean any of these, & justifiably bases on these & similar facts a generous view of the termination's capabilities; credible meaning for him worthy of credence, why should not reliable & dependable mean worthy of reliance & dependence? [Fowler]
In Latin, -abilis and -ibilis depended on the inflectional vowel of the verb. Hence the variant form -ible in Old French, Spanish, English. In English, -able tends to be used with native (and other non-Latin) words, -ible with words of obvious Latin origin (but there are exceptions). The Latin suffix is not etymologically connected with able, but it long has been popularly associated with it, and this probably has contributed to its vigor as a living suffix.