As you are waiting you might be interested in this earlier thread by u/Iphikrates, focused on gods associated with warfare

I'm still a student in the subject so if any experts come along with more complete answers I would recommend their's over mine, but I can at least point out a few things.

While the modern idea of the Hellenic gods often attributes a single, specific sphere of influence (Athena for wisdom, Zeus for Justice, Poseidon for the Sea, etc.) it was more complex than this and the gods had multiple 'duties', for instance Poseidon was also regularly associated with horses, earthquakes and many other areas. With such a vast list of duties, crossovers and muddled areas where multiple gods were attributed to the same field are inevitable and ways of distinguishing which element of the god you required became very important. As the comment here on Athena Promachos (I like to translate it as Athena of the Front Lines) demonstrates: the gods were often attributed epithets to indicate which element of the god's influence was being called upon. Zeus, for instance, while being more generically known as the king of the gods, the god of justice, or the god of the sky was also a god of marketplace deals/oaths (Zeus Agoraios), a god related to Athenian phratries (Zeus Phratios), the god of Xenia and the customs of treating guests, etc. All of these epithets represented different sides of the same deity, however, they would often be represented differently depending upon the epithet. The best example of this would be Athena's statues on the Acropolis, the main large bronze statue was of Athena Promachos, she was appropriately armed with her spear, shield and helmet to show the martial nature. Whereas another statue found in the Erechtheion was of Athena Polias (Athena the protector of the city), although we have no archaeological remains of this statue (as even in the 5th century this wooden statue was considered ancient and I have seen some suggest it may have been carved as far back as the Mycenaean period) it is often assumed that it emphasised more peaceful and feminine traits such as golden jewellery, a libations bowl, and a lack of weapons and armour.

You may be thinking that this could get confusing or overwhelming with the many epithets each god held and you would not be alone in this, one of the questions regularly asked of prophets and oracles by the ancient Greeks was which god and which aspect of a god should they pray to in a specific circumstance. For instance if you planned to open a stall in the Agora would you make a sacrifice to Hermes, who is considered the god of traders, or to Zeus Agoraios?. An example of this can be found in Xenophon's Anabasis (3.1.5 - 3.1.8) in which he consulted the oracle of Delphi as to which god he should offer his prayers to for a naval expedition.

The direct answer to your question is a resounding "kind of", there were specific focuses of gods which were more well known, however, there was a much deeper and more nuanced collection of epithets which demonstrated a far broader focus than a simple "God of War", "God of Wine" etc. These were undoubtedly major parts of their sphere of influence, but they did not represent all that they stood for. All of this is without even mentioning the differences between the more universal influences of gods, which all of the Greek world recognised and prayed to, and the more local/personal cults which could differ wildly in focus and may only be celebrated in one region, one polis, or one family. As with most popular ideas there is a nugget of truth but the answer is far more complicated and nuanced.

(Edited a few mistakes of phrasing and grammar and added a few extra details)

While you wait, you may be interested in this answer by u/Steelcan909

Dionysus: Myth and Cult by Walter Otto touches on this. He believes that it is indeed an oversimplification. Dionysus, for example was known as the god of the vine, a god of death, the god who arrives, the hidden god, and many, many other names. He represented a wide variety of aspects of Ancient Greek life and could be considered the counterpart to Apollo. Viewing him this way, he becomes a god of all that is animal and natural or earthly in juxtaposition to the golden, ordered civilization that is the realm of Apollo. Yet, if you google Dionysus it will likely say that he is simply a god of nature or vegetation. Otto believed that this was an egregious oversimplification which stripped him of his many aspects and meanings for Ancient Greek people.