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I understand these phrases have basically the same meaning. If so, why does the former have an indefinite article and latter no article? Any logical explanation?

According to Merriam-Webster's Dictionary:
HASTE -
rash or headlong action :
She sent the letter in haste and later regretted it.

IN A HURRY -
without delay : 
as rapidly as possible:
the police got there in a hurry.

But nowadays it is possible to use 'in a haste' as well.
One of numerous examples from Reverso.context.net:
'I wish I could bring you a picture, but I was in a haste'.

In haste does not generally take the indefinite article because it was borrowed directly from Old French en haste (ModFr en hâte), the preposition varying in Middle English among in, an, or on.

Hurry, however, as verb or noun, is first attested in Shakespeare:

His remedies are tame i’ the present peace

And quietness of the people, which before

Were in wild hurry. — Corialanus 4.6.

While Shakespeare used no article, in a [state of] x is a common pattern in English: in a rush, lather, dither, rage, etc. Curiously enough, the article does not make the noun denoting that state countable. If you were in a hurry yesterday morning and again in the afternoon, you weren’t *in hurries yesterday.

and being soone after aduertised of the proclamation, he came forth in a hurry: — Francis Bacon, A declaration of the practises & treasons attempted and committed by Robert late Earle of Essex, 1601. EEBO

Could Laureate Dryden Pimp and Fry’r engage,

Yet neither Charles nor James be in a rage? — Alexander Pope, “Satire I, Imitations of Horace,” Works of Alexander Pope, Esq., vol. IV, London, 1751, 67.

… smoothing discords which would have left your man of affairs in a dither … — H. J. Massingham, The friend of Shelley; a memoir of Edward John Trelawny, New York, 1930.

In a haste arose to conform to this pattern:

whan men doo thynges in a haste … — Gulielmus Gnaphaeus, John Palsgrave, trans., The comedye of Acolastus translated into oure englysshe tongue, 1540. EEBO

Would not a iuſt ſovereign rather deify theſe, knowing who are the beſt of men, and not ſhut heaven in a haſte … — Robert Millar, The History of the Propagation of Christianity and Overthrow of Paganism, London, 1731, 24.

To judge by a Google search, the most frequent use of in a haste occurs today among speakers in India, Africa, and in International English, though there are still a few American and British writers who favor it.

As the conflict rages, indications are that the National Assembly may not be in a haste to look into the matter. — Newswatch: Nigeria's Weekly Magazine, 2006.

Sir, today, if we do anything in a haste, again and again, I am saying, if we just go around in a haste without getting these credentials and facts and figures, it would not stand in a court of law. — Parliament of India, 2006.