Hi grSeva,
When you exert a force to bring something closer to you, you exert a "pull" on that object. For example, you need to "pull" your car door in order to open it. When you are inside the car, you "pull" your car door to close it. Both actions bring the car door closer to you.
When you [drag] something, you are also exerting a "pulling" force. This is the similarity. However, when something is very heavy and you need a great deal of effort to "pull" it (usually across the floor or a surface and for a longer time), this is when you are "dragging" it. This is a difference.
"Drag" can also be used to express an unwillingness to move. For example, my dog hates baths, and I have to "drag" him to the shower room.
I hope this clears the air.