Allusive refers to a statement or reference that is suggestive, rather than mentioning something in a straightforward manner. Related words are allusively, allusiveness, allusion. The adjective allusive appears in the early 1600s, from alludere meaning a playing with, a reference to.
Illusive means not based on reality, deceptive. Related words are illusively, illusiveness. Illusory is interchangeable with illusive, related words are illusorily, illusoriness, illusion. Illusive appears in the early seventeenth century from the Latin illusivus to play with, mock at.
Elusive means difficult to catch, to find, to remember. Related words are elusively, elusiveness, elude. Elusive comes into the English language in 1719 from the Latin eludere, meaning elude, frustrate.
Strangely, “The Black Cat” is an allusive masterwork of political cinema. (The New Yorker)
If that brings you as close to tears as it brought me, you’ll understand that Ms. Anderson’s delicately allusive methods can open you up to feelings you didn’t expect to feel—as in her quietly piercing remembrance of what may have been the only moment of her life when her mother truly loved her. (The Wall Street Journal)
Predatory fish include my infamous and illusive muskie, which I’ll now be chasing on the nastiest days. (The Bowling Green Daily News)
Furthermore, in addition to focusing on the standard measures – GDP, per capita GDP, or household incomes – he combines data on health with income to create a more holistic perspective; this new approach enables him to assess more rigorously the illusive concept of wellbeing. (Forbes)
Hungary’s foreign minister says effective solution to migrant crisis still elusive (USA Today)
Frank Ocean, the elusive, indefinable guard of modern R&B, was supposed to come out with his second album in July. (The Stanford Daily)