Yeah the range defines how far you can summon them, in other words Short range from you. But they can fly as far as they want.
Now this technique, you already performed at the start with a smaller Crow. No need to summon it again, just posting it so you know you can use it. In this case however, the Crow is much larger, akin to Sasuke's Hawk in his fight against Danzo even.
(Kuchiyose no Jutsu: Kuroi Karasu) - Summoning Technique: Black Crow
Rank: B
Type: Supplementary
Range: Short
Chakra cost: 20
Damage points: N/A
Description: The user will summon a large black crow that stands about as tall as two people with a wingspan of about 5 meters which can be used for various tasks in combat such as generally attacking the opponent or for maneuvering around on the battlefield. The crow itself is only capable of standard physical attacks using its claws, beak and wings.
Note: can only be summoned once
So let's move onto the next one:
(Karasu Bunshin no Jutsu) - Crow Clone Technique
Rank: C
Type: Supplementary
Range: Short
Chakra cost: 15
Damage points: N/A
Description: A technique that produces a clone by projecting one's own chakra towards dozens of crows. These are summoned by the technique itself. Because it uses crows as a medium, it requires less chakra than the normal Shadow Clone Technique, while still being able to perform techniques (up to A-Rank). The dozens of crows come together to form the body of a clone. When the chakra projected by the user is severed, the crows disperse, though the user is still able to continue to speak through it.
Note: Can only be used by signers of the Crow contract and can only make 2 clones with each use.
We are all familiar with the Bunshin technique. Well this is a variation of it, by emitting your chakra into dozens of crows that you summon using this technique, they come together and form a copy of yourself. The good thing about this Bunshin is that it requires less chakra, something vital in NW activities, while being able to perform up to A rank techniques. Don't lose focus or get your chakra cut off as the clone will break apart into a swarm of wild crows and no more.