Witchcraft and Wizardry mean the same thing, the only difference being who is doing it. Simply: it's witchcraft when a witch does it and wizardry when a wizard does it. There's nothing more to it than that.
Wizard and its derivatives often functions as the generic he in the Harry Potter series. See for instance the name "the Wizarding World". There are also gender neutral expressions like "magical".
Hogwarts could have been titled with the generic he (Hogwarts School of Wizardry) or in a gender neutral way (Hogwarts School of Magic). But could doesn't equal must or even should.
Just as in the real world we don't make exclusive use of the generic he/gender neutral titles, neither does the Wizarding World. Much as you might say, 'greetings ladies and gentlemen' rather than 'greetings guests', the Wizarding World might say 'greetings witches and wizards'.
The titling of Hogwarts is no different and perfectly correct. We might speculate why they choose to name it so (my guess is to emphasise that this was a co-ed school which otherwise might get lost) but that would be speculation beyond your question.
Some evidence for the use of wizard as a "generic he"
Wizard is used to refer to genderless magical things quite often. For example:
Harry was turning over the wizard coins and looking at them. He had
just thought of something that made him feel as though the happy
balloon inside him had got a puncture. - HPPS
“They didn’ keep their gold in the house, boy! Nah, first stop fer us
is Gringotts. Wizards’ bank. Have a sausage, they’re not bad cold —
an’ I wouldn’ say no teh a bit o’ yer birthday cake, neither.” - HPPS
"Don’t you think it’s a bit odd,” said Harry, scrambling up the grassy
slope, “that what Hagrid wants more than anything else is a dragon,
and a stranger turns up who just happens to have an egg in his pocket?
How many people wander around with dragon eggs if it’s against wizard
law? Lucky they found Hagrid, don’t you think? Why didn’t I see it
before?” - HPPS
Photographs (and notice this one explicitly includes a woman).
It seemed to be a handsome, leather-covered book. Harry opened it
curiously. It was full of wizard photographs. Smiling and waving at
him from every page were his mother and father. - HPPS
It is also used to refer to groups of both witches and wizards. For example here:
“Are all your family wizards?” asked Harry, who found Ron just as
interesting as Ron found him.
“Er — Yes, I think so,” said Ron. “I think Mom’s got a second cousin
who’s an accountant, but we never talk about him.” - HPPS
Derivatives are also common and used in a gender neutral way.
For example: Families
“I really don’t think they should let the other sort in, do you?
They’re just not the same, they’ve never been brought up to know our
ways. Some of them have never even heard of Hogwarts until they get
the letter, imagine. I think they should keep it in the old wizarding
families. What’s your surname, anyway?” - HPPS
Quidditch, the most popular sport in the wizarding world (six tall
goal posts, four flying balls, and fourteen players on broomsticks). - HPCS
Exams taken by both girls and boys
“Wish I knew what he was up to,” said Fred, frowning. “He’s not
himself. His exam results came the day before you did; twelve O.W.L.s
and he hardly gloated at all.”
“Ordinary Wizarding Levels,” George explained, seeing Harry’s puzzled
look. “Bill got twelve, too. If we’re not careful, we’ll have another
Head Boy in the family. I don’t think I could stand the shame.” - HPCS