Etymology
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speciality (n.)
early 15c., "a special quality or thing;" mid-15c. as "quality of being special," from Old French specialte, especialte "nature, special quality, particularity; special point, distinction," and directly from Latin specialitatem (nominative specialitas) "peculiarity, particularity" from specialis "individual, particular" (see special (adj.)). French form spécialité (especially in reference to restaurant dishes) is recorded in English from 1839.
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specialty (n.)
c. 1300, "particular affection; special attachment or favor, partiality," from Old French especialte, more vernacular form of specialite (see speciality). Compare personalty/personality; realty/reality. From early 15c. as "unusual, or extraordinary thing; specialized branch of learning; peculiar quality, distinctive characteristic."
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-ality 

word-forming element; see -al (1) + -ity. Originally also in reduced form -alty, especially in words from French (mayoralty, etc.), hence the occasional doublet such as fealty/fidelity, realty/reality, specialty/speciality, loyalty/legality.

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spirituality (n.)

late 14c., spiritualite, "the clergy," also "ecclesiastical property; things pertaining to the Church," from Anglo-French spiritualite, Old French espiritualite, and directly from Late Latin spiritualitatem (nominative spiritualitas), from Latin spiritualis (see spiritual). Meaning "quality of being spiritual" is from c. 1500; seldom-used sense of "fact or condition of being a spirit" is from 1680s. Also in early use spiritualty (late 14c.).

English is blessed with multiple variant forms of many words. But it has made scant use of them; for every pair historic/historical; realty/reality, or luxuriant/luxurious there is a spiritualty/spirituality or a specialty/speciality, with two distinct forms, two senses requiring differentiation, hundreds of years gone by, and but little progress made in in sorting them out.

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