‘Dark wizard’ usually means ‘evil wizard who uses Dark magic’.
Everyone described in the books as a Dark wizard is also considered an “evil” wizard. Though the term “Dark wizard” is often used in abstract to describe unnamed threats or wizards who engage in certain practices like creating Inferi or Horcruxes, the two named wizards who are specifically referred to as Dark wizards are Lord Voldemort and Grindelwald. While there may be “good” or “neutral” wizards who have used some Dark magic, there’s no instance of them being actually referred to as Dark wizards - the term seems to always be used specifically for those who use Dark magic and are also considered evil.
Hagrid is most likely just generalizing, so it’s later phrased as “Slytherin had more Dark wizards than the other houses” to make it a more accurate statement.
Dark magic use won’t instantly define a person as a Dark wizard.
Using some Dark magic doesn’t automatically classify someone a Dark wizard - there are instances of “good” or “neutral” wizards using magic considered Dark, such as when Harry and McGonagall use Unforgivable Curses. Despite this, it’s unlikely anyone would term them as Dark wizards.
This is also implied by Professor Binns when discussing the legend of the Chamber of Secrets.
“But, Professor,’ piped up Parvati Patil, ‘you’d probably have to use Dark Magic to open it –’
‘Just because a wizard doesn’t use Dark Magic, doesn’t mean he can’t, Miss Pennyfeather,’ snapped Professor Binns. ‘I repeat, if the likes of Dumbledore –”
- Harry Potter and the Chamber of Secrets, Chapter 9 (The Writing on the Wall)
He implies that the teachers could have used Dark magic to open the Chamber.
It’s also possible to be “bad” without ever using any Dark magic.
The term “Dark wizard” only seems to be used to refer to evil wizards who use Dark magic. It doesn’t seem to be used if a wizard is “bad” but without using Dark magic. For example, Lockhart did bad things, but did them using Memory Charms, which don’t seem to be considered Dark at all.
“I had to track these people down. Ask them exactly how they managed to do what they did. Then I had to put a Memory Charm on them so they wouldn’t remember doing it. If there’s one thing I pride myself on, it’s my Memory Charms.”
- Harry Potter and the Chamber of Secrets, Chapter 16 (The Chamber of Secrets)
However, wiping other wizards’ memories so he could take credit for their accomplishments was certainly wrong of him, so he would be considered bad but not considered a Dark wizard.