Are owls in the Harry Potter universe normal ones?

The owls in the Harry Potter universe are really impressive. They are much much smarter than the real world carrier pigeons (RFC 1149). They are able to find a specific person and can collect money for newspaper delivery. They can also fly in daylight unlike real world owls.

Are they magical cousins of owls we know? Or, are they magic-fied normal owls?

Answer

Owls wouldn’t be magical creatures - they’re not hidden from Muggles, whereas all magical creatures (even less obviously magical ones like Kneazles which are basically very smart odd-looking cats, Plimpies which are unusual fish, and the Flobberworm, whose only remotely magical attribute that’s mentioned is that its mucus can thicken potions) are hidden. We know owls aren’t hidden from Muggles, because the Muggles notice when owls begin flying in the daytime, and they know enough about owls to know the difference between usual and unusual owl behavior.

“When Dudley had been put to bed, he went into the living-room in time to catch the last report on the evening news:

‘And finally, bird-watchers everywhere have reported that the nation’s owls have been behaving very unusually today. Although owls normally hunt at night and are hardly ever seen in daylight, there have been hundreds of sightings of these birds flying in every direction since sunrise. Experts are unable to explain why the owls have suddenly changed their sleeping pattern.’ The news reader allowed himself a grin.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy who Lived)}}

Having magical creatures noticed by Muggles is a violation of the Statute of Secrecy, and would result in punishment for the governing body that allows such a thing to happen under their watch.

“In 1750, Clause 73 was inserted in the International Code of Wizarding Secrecy, to which wizard ministries worldwide conform today:

Each wizarding governing body will be responsible for the concealment, care, and control of all magical beasts, beings, and spirits dwelling within its territory’s borders. Should any such creature cause harm to, or draw the notice of, the Muggle community, that nation’s wizarding governing body will be subject to discipline by the International Confederation of Wizards.”
_{^{- Fantastic Beasts and Where to Find Them}}

Muggles are allowed to notice owls, meaning they’re not magical creatures. However, the J.K. Rowling writing on Pottermore about owls says it’s possible that owls have an innate bent for magic. The delivery owls are indeed “normal” owls, not a special magical subset.

Whether because they possess an innate bent for magic (just as pigs are reputed to be innately non-magical), or because generations of their ancestors have been domesticated and trained by wizards and they have inherited the traits that make this easy, owls learn very quickly, and seem to thrive on their task of tracing and tracking the witch or wizard for whom their letters are intended.
_{^{- Owls (Pottermore)}}

Owls are trained to deliver letters, but the wizards who train them don’t fully understand their tracking abilities or how exactly they find the intended recipient.

The mystical association between the name and the human who bears it has long been understood by witches and wizards of all cultures. While the process remains mysterious even to those who train up owlets to become wizarding pets or postal owls, the birds appear to be able to make such a connection between the name and its possessor that enables them to trace the witch or wizard concerned wherever he or she may be. An owl does not need to know an address, although witches and wizards generally add the place to the envelope on the off-chance that the owl is intercepted and the letter falls into other hands.
_{^{- Owls (Pottermore)}}

In addition, almost all owls are owned by either an individual or the Owl Postal Service.

So numerous are the owls employed by wizards worldwide that it is generally safe to assume that virtually all of them are either the property of the Owl Postal Service of their country, or of an individual witch or wizard.
_{^{- Owls (Pottermore)}}

Therefore, the owls that Muggles see are very likely to be the same ones delivering wizards’ mail.