A and B are playing a game. A scores (verb) one point. B scores 2 points. A scores one point. A scores another two points. A has scored 4 points B has scored 2 points. The score (noun) is 4 – 2.

Score can be a noun or a verb. You score points. And you want to know what the score is (the sum of the points for teams usually). Point is only a noun. Points are like the details that add up to the score.

点 = point 取れる = score