Jumping to conclusions is a phenomenon where people reach a conclusion prematurely, on the basis of insufficient information. For example, a person jumping to conclusions might assume that someone they just met is angry at them, simply because that person wasn't smiling at them while they talked, even though there are many alternative explanations for that behavior.
In our daily lives, we're constantly hearing or making persuasive arguments. We may be listening to a colleague's argument for why we should support one of her initiatives. We may hear an argument for why we should buy a certain product. Or we may need to make our own argument to get approval for one of our projects.
Cherry picking is a logical fallacy which occurs when someone focuses only on evidence which supports their stance, while ignoring evidence which contradicts it. For example, a person who engages in cherry picking might mention only a small number of studies out of all the studies which were published on a certain topic, in an attempt to make it look as if the scientific consensus matches their stance.