What is the difference between the normal weight training motions (e.g. bench press lifting it up and down) and holding a weight at a certain point (e.g. holding a weight in the middle of a press for a long amount of time)? Why is the first more effective? Does the second have any specific benefits that you could elaborate on?
Dave Liepmann is correct. However, the concept is called Isometric hold vs. Full Range of Motion.
Full Range of Motion exercises are more functional and have been shown to reduce stress on the joints. In this case, it's the shoulder the the elbow joints. Isometric hold has been shown to recruit more muscle fibers, but also increase stress on the joints (shoulders and elbows with bench press).
This is because our body and joints are more suited for full range of motion with our daily activities. Think about it, we tend to get up and move, pick up things and put them down, constantly moving from one place to another.
With this being said, there is nothing wrong with training with Isometric hold, just as long as you have a goal and is functional and specific to that goal. If your goal is to recruit more muscle fibers, then you should try to train with Isometric hold every now and then. I say 1-2 times per month to reduce stress on the joints (squats, bench presses, shoulder presses, etc.). It takes time to get used to this type of training methodology.
A good example is to look at the way most offensive linemen train. They do train with Isometric hold (typically for about 5-10 seconds) to give their running backs and quarterbacks sometime to work with.
All in all, just making sure the training methodology is suited for your goals and is functional to your activities, whether you are a runner, weight lifters or any athlete to reduce injuries and for best results.