fps is the time between exposures, shutter speed is how long the shutter is open, typically they are not the same, of course the shutter speed must be < 1/fps. Rather than refering to a particular shutter speed when talking about video most people talk about shutter angle, which is basically a percentage of time the shutter is open during one frame period (1/fps). There is a common rule of thumb known as 180 degrees, this just means you should have the shutter open 50% of the total period of the frame (they talk in degrees instead of percent which I think is silly, but you get the idea). So in your example 60fps and 1/120 shutter, this would be a 180 degree shutter. This rule is pretty good most of the time, but there are a couple of good reasons to violate it. One of those reasons is if you are shooting something intended to be slow motion. When you know you are going to shoot slow motion you want as little motion blur as possible (normal a little motion blur is desireable, hence the 180 rule). But when slowing footage down, it looks bad. Also, the software plugins that can interpolate frames and slow down your footage even more, work better when there is less motion blur, so to help them out make the shutter as fast as you can.
Here's an example of 180 degree shutter. F means start of a new frame, O means the shutter is open, C means it is closed (BTW, in video the shutter is electronic not mechanical, so it's not like the entire sensor is turned on in one instant, it actuall has to go line by line, this creates the undesirable rolling shutter effect):
FOOOOCCCCFOOOOCCCCFOOOOCCCCFOOOOCCCC