These are two definitions for the noun "determination" from the same dictionary (American Heritage® Dictionary). One was right below the other. Is it me or you could basically combine these two definitions (2.a with 3.b & 2.b with 3.b) into one and there isn't any real difference between them?
2. a. The ascertaining or fixing of the quantity, quality, position, or character of something: a determination of the ship's longitude; a determination of the universe's mass.
b. The result of such ascertaining.
3. a. The act of making or arriving at a decision: After long determination, she decided to move to Utah.
b. The decision reached: It is my determination to sell the house.
See Synonyms at decision.