In the first sense, both mean grading or assessment. As for score, it is usually a numerical record of a competition, but you can get scores in a game or for a test. In other words, score is a result expressed with numbers. The meaning of point is more extended. In Geometry, for instance, it is a dimensionless object. We use point as punctuation mark. The word can be found in expression, like point of view meaning aspect, the main point, meaning the essence of something.
