I suppose one way of looking at it is that a single shot with a bow isn’t deadly enough to kill (or drive off) significant monsters in one shot, so when you start using your weapons on things, you’re picking a fight.
According to the rules (p. 67), whenever players engage with a monster in an important way, it’s a conflict. As GM, you need to ask the players what they’re trying to do. Are they trying to kill it? Drive it off? Just see how tough it is?
As GM, it’s your call when the condition, “in an important way” has been satisfied. These all strike me as legit:
Scenario 1
GM: A giant spider hangs in its web, slung across the corridor.
PC: I shoot it with my bow!
GM: What are you trying to do?
PC: Well, kill it.
GM: Buckle up - you’re now in a Kill Conflict.
Scenario 2
GM: A giant spider hangs in its web, slung across the corridor.
PC: I shoot it with my bow!
GM: Your arrow lodges in its carapace, and the thing lets out a wet hiss. It drops to the floor and begins scuttling away from you. What do you do?
PC: We chase it!
GM: Okay, it’s a Flee Conflict.
Scenario 3
GM: A giant spider hangs in its web, slung across the corridor.
PC: I shoot it with my bow!
GM: Your arrow lodges in its carapace, and the thing lets out a wet hiss. It drops to the floor and begins scuttling toward you. What do you do?
PC: Oh crap, quick, Cedric, hit it with your magic!
GM: What are you trying to do?
PC: Stop it from getting to us.
GM: Okay, it’s a Drive Off Conflict.
Scenario 4
GM: A giant spider hangs in its web, slung across the corridor.
PC: I shoot it with my bow!
GM: Your arrow lodges in its carapace, and the thing lets out a wet hiss. It drops to the floor and begins scuttling away from you. What do you do?
PC: We chase it. Don’t let it get away!
GM: You’re faster than it; you move past its web and you’re upon it, it turns and raises its forelegs at you menacingly. Venom drips from its fangs as they spread wide.
PC: Kill it!
GM: Okay, it’s a Kill Conflict.
But saying, “I want to kill it without starting a conflict,” isn’t allowed, it’s a bit like saying you want to get hurt without losing any hit points. Killing something is a fictional event, and Conflict is how you find out if you get to do it.
As GM, you’re free to declare that this particular giant spider is such a pushover that it’s easy to take it out with a single arrow or sling stone. But if it’s a statted-up monster and the party doesn’t have some special immunity to retaliation (e.g. they’re behind teflon fortifications the spider couldn’t conceivably climb) then Conflict is how you find out what happens.