First, the name oracle covers all cards. The word oracle means “to divine” and this can be done with both tarot and oracle decks.
The biggest difference between these two deck styles is how they are interpreted by the reader. Tarot decks are much more structured and the cards often have universal meanings. Angel and Oracle cards are more free form and are read intuitively. Both types of cards are useful depending on your level of expertise and your ability to tap into Spirit/The Voice of the Universe.
Tarot decks have 22 major and 46 minor arcana cards. Think of this as face cards and numbered cards. These decks are arranged in suits and have 78 cards per deck. The meanings of each card (7 of cups or the Hermit card for example) are similar between decks no matter the style. Readings with tarot will give more detailed and deeper answers to your questions.
Oracle decks can have as few as 20 cards in a deck and as many as 50. These types of cards have different stand-alone images or themes, for example a dragon, fairy or dream deck, and the reader intuits the meaning based on the question asked in the reading and the image that appears in the spread. This allows for Spirit to speak in a more freeform manner. Because oracle cards are simpler to read they are often good for beginners.
Both types of decks have a language of their own. A person buying a deck will often choose images that call to them or make them feel comfortable or connected. This is important so that the reader is open to the spiritual messages being conveyed.
As a side note, it’s not true that your deck needs to be gifted to you. This belief comes from a time when decks were not commercially printed and were often hand drawn so finding them was difficult and shrouded in mystique. It also would allow the person gifting the deck to help teach you. While this is nice, it’s not necessary. There is nothing wrong with finding and buying the deck that resonates with your style!