Handline

they say Handline (Casters) but it's just basically a Drop rig with a sinker and 2 or 3 hooks or no sinker depending on how you're fishing and what type of fish you're targeting. in the caribbean there's not much confidence in Rods especially for the bigger fishes because the fishes here are different (so we believe) they quickly suck in your bait and spit it out and if you're not holding the line in your hand you may miss that opportunity to set the hook. 

What is round hooks are used...aren't they better for such kind of fishing? Itsa, what is your opinion....

I am not sure, I have never tried this style of fishing.

Circle hooks are designed to make it very difficult, almost impossible for the fish to throw the hook. I would imagine that using a circle hook would be better.

When using a rod, the rod keeps pressure on the hook. If the fish swims directly towards you the pressure is lost but there is plenty of time to lift or pull back and regain the pressure. In most cases it would not be much more than 1 second.

With a hand line, if the fish swims directly at you, you have to pull in the line to regain the pressure. This would add several seconds which is more than enough time for the fish to throw the hook.