The two different interpretations you are referring to are known as a strict and loose interpretation of the Constitution. Here is more information about both.
1) Strict interepretation- Individuals who favored a strict interpretation of the Constitution stated that in order for Congress or the President to act, the right they would be performing must be written into the US Constitution.
2) Loose interpretation- Individuals who favored a loose interpretation of the Constitution stated that the Constitution is flexible and there is room for broad interpretation. Essentially, these people argued that some powers in the Constitution are "implied."