See, for me, 'agility' is a combination of lower body strength, endurance, kinesthetic sense, athletic training, ability to shift weight effectively, and being low-mass in general. It's generally big moves, performed rapidly (moving legs fast to run, twisting body quickly to dodge).
Manual 'dexterity' on the other hand is almost exclusively upper body, fine control with hands, in general small moves performed slowly.
Taking a snap shot with your crossbow at a goblin who just jumped out from behind a tree ten feet away, that would conceivably be agility. You're making a big movement, twisting at the hips and shoulders as much as anything. Your skill helps you know where to bring that crossbow up to firing position, but the key is to get it there fast and then shoot.
Aiming at a goblin a hundred feet away--even if he's charging--is a long term action, though. For one thing, your crossbow is probably already drawn, so there's no big actions there. It's not all that time critical...it's not a matter of "will he hit me before I can shoot". Instead, it's "How long will it take me to aim as perfectly as I can". It needs small movements, and it takes nerves of steel--that's mental, sure, but physical training also keeps your hands from shaking. That's dexterity.
I'm not sure what I'd say about a task like, oh...kicking a football. Clearly that has a lot of agility. Clearly it has a lot of kinesthetic sense. I'm not sure if a task like that would need dexterity, though...probably not.
Sitting at a workbench and slowly chipping away at a rock mug, on the other hand--You really don't want your hand to slip.
Hunh. The more I look at those definitions, the narrower my description gets. At this point I have to say dexterity is almost exclusively "ability to keep hands from shaking/slipping". But there's a lot of tasks that make that important!