Stags and does don't mate. [The eternal stag/doe debate]
A Patronus Charm is cast based on a powerful memory. A powerful memory, of course, does not have to equal a happy one, as is evident when Harry casts his first Patronus thinking about his parents while not knowing if the memory is even real.
For Severus, it is a similar case. He’s the only known former Death Eater who can actually cast a Patronus, meaning he, too, holds a powerful memory to help him cast it. I personally believe that this particular powerful memory is also the first one Harry sees after Severus gives him his memories as he lay dying. It was of meeting Lily on the playground that day. It wasn’t a particularly nice memory, as she rejected him telling her she’s a witch and ran off. But it was also the day that marked the moment that he knew he was not alone in Cokeworth. There was someone out there like him, and it gave him hope in a way he had not known hope before.
Stags and does (particularly white harts in historical documents, which is another nod towards the Patronuses) were holy creatures that guided people on their quest in search of the holy grail (Hufflepuff’s cup), such as the story of Lancelot and his sword Excalibur. Severus’s doe directly correlates to that in the chapter where he uses his Patronus doe to guide Harry to Gryffindor’s sword in the lake. In the story of Lancelot, it was the Lady of the Lake who gave him Excalibur, which he could then use to continue his quest. The same thing applies to Harry in a different setting.
Now, here’s a more fun fact. In British English, there’s an important distinction between stags and does. To make it understandable, I made an overview of the six different types of deer known in the UK and their terminology.
Species Male Female Young
Red Stag Hind Calf
Sika Stag Hind Calf
Roe Buck Doe Kid
Muntjac Buck Doe Fawn
Fallow Buck Doe Fawn
Chinese water deer Buck Doe Fawn
Notice anything funny? Stags and does don’t mate because they are not the same type of deer. They are similar, but they aren’t compatible. That also leaves the question on whether Severus and Lily had the same doe. Were they the same ones in a “same soul” type of situation, or did Lily have a Fallow and Severus a Roe for all we know? In the movie Severus’s doe seemed like a roe deer. Harry’s stag was modelled after a red stag.
Of course, stag, doe and fawn are the most commonly used terms, and most people probably aren’t aware of the correct terminology. I wouldn’t be surprised if Rowling wasn’t aware of it either (but then again, she was also an English major in college and an expert at writing subtle hints and plotpoints). However, I do think that Rowling wants us to believe that James’ stag and Lily’s doe are connected somehow, but there are many Patronus cases in canon where Patronuses don’t have to correspond to each other in case of relationships (just think of Ginny’s horse, Ron’s Jack Russel and Hermione’s otter. More simply put, Rowling didn’t entirely think it through when she did the whole stag/doe thing and we’ve been left guessing how it works since 1999.
But personally, of course, I’d like to believe that Severus and Lily have a doe because the Patronus stems from the same powerful memory. Their meeting on the playground that day equally changed their lives for good.
Personally I always headcanoned that the Patronus is fueled by a memory of love, not happiness (this misunderstanding in-universe is why people struggle with it, because they are trying to use memories of joy). It also explains why the spell utterly backfired on a Dark wizard in extracanonical material: they were using a memory of when they were happy, but a memory of *hate*. For this reason I always imagined the Malfoys as being able to use the spell if they were to do a genuine attempt at it: whatever their faults, they love each other as a family.
And yeah, I always liked to imagine the close relation to James and Lily's Patronus forms as a coincidence. And that the reason Snape and Lily share Patronus as being a result of them using *the exact same memory* when casting it, a memory of when they were children.
You choose to forgot one thing. Harry first patronus was an incomplete attempt. Snape memory was defensive and protective and harry afterall his patronus was full fledged.
There is a deep difference.
There is an article on pottermore that goes deeper into this.
