The projectile hitbox is one kind of attack hitbox; it is associated with projectiles.
The finer details are different from game to game, but common factors include being unsusceptible to traps, and not having a damage hitbox.
Other than those, they resemble strike hitboxes, and will occasionally be classified as such.
However, even among strike hitboxes, there are things without damage hitboxes, so unless someone tests traps, there may actually be no way of differentiating them.
These have a projectile hitbox, but they do not truly come free from the body, and by appearance, there are moves that do not appear to be projectile in nature.
These are not affected by reflecting moves. In this case, the attack hitboxes for both sides will usually disappear.
They are not affected by traps, either, which make them more convenient for zoning, anti-air, and smashing emergency evasions.
On the other hand, there are some moves that look just like unlaunched projectiles (e.g., the character’s hand may be seen in the midst of a blaze), and yet have a strike hitbox.