I'd assumed (probably due to lots of mmo's) that the attack number (the big one) is more of a damage per second calculation result.
So your hand cannon with 100 dmg and 4/5 impact might hit like a truck, but in the same time frame the auto rifle with 150 attack and 1/5 impact will do more damage (assuming you hit with each bullet).
But your point of clarity is still a perfectly valid one.
@probablytuna: my understanding is the bigger icon with the fancy symbol is a boss type mission. rather than a standard "go here press button and kill everything" it's "go here press button and kill everything until we give you the boss". but i'm sure others will have more informative descriptions.