Usage patterns
〈物〉の動きを見るto watch the movement of something
I was watching the bird's movements intently.
〈事〉の動きを注視するto closely watch the trend/development of something
I'm closely watching the movements of the market.
〈物〉の動きが速いsomething's movement is fast
The player moves so fast I can't follow with my eyes.
〈事〉の動きを見せるto show signs of a trend or change
There are signs of an economic recovery.
〈場所〉で動きがあるthere is activity/development happening in a place
There's a new development happening in the political world.