Table 6-1 on pg 205 of the EotE core rulebook lists the skill check difficulty for ranged attacks.

So then, what does the weapon's range have to do with it (if anything)? e.g., Blaster Rifle = Range Long; Slugthrower Pistol = Range Short. Is this simply the max range of the weapon (e.g., a slugthrower pistol cannot be fired at targets at medium or further range)?

Yep it's the Max range for that weapon.

You're correct. The range listed is simply the maximum range of the weapon.

If you're concerned about that meaning players have no reason to go with anything other than the biggest gun with the longest range, remember that they might be forced to check all but personal defense weapons (read: Ranged [Light]) at the door or on their ship. Also, wielding a Ranged (Heavy) weapon while Engaged adds two Difficulty dice, compared to Ranged (Light) at one.

You're correct. The range listed is simply the maximum range of the weapon.

If you're concerned about that meaning players have no reason to go with anything other than the biggest gun with the longest range, remember that they might be forced to check all but personal defense weapons (read: Ranged [Light]) at the door or on their ship. Also, wielding a Ranged (Heavy) weapon while Engaged adds two Difficulty dice, compared to Ranged (Light) at one.

Another reason for using pistols is the "Rule of Cool", dual wielding and going all John Woo on a group of Stormies.

As I recall the long-range slugthrower rifle gets a setback for shooting at close range