DE: Resistant force, 2 equations

[rocomath]

So I'm given two equations, but not really told when it's appropriate to use one over the other.

1) The resistance is proportional to the velocity

$$F=-mg-rv$$

2) The magnitude of the resistance is proportional to the square of the velocity

"the magnitude" ... what's the difference?

$$F=-mg-k|v|v$$

 

[gabbagabbahey]

Are some of these quantities suppose to be vectors?