Writer credits are complicated, and unparsing them for any particular project may be an impossible task without talking directly to those involved. Every detail matters: “&” and “and” mean two different things, for instance (writers connected with “&” are a writing team, while those connected with “and” are not).
Generally, different credits represent how much of what you see on screen came from any particular writer. The WGA credits page has detailed breakdowns of the credits, and should have answers to any related questions that may arise.
Credits have different long-term value attached to them, as residuals and money paid to a writer from the future exploitation of a film are based on the credit that writer received. This is why writers often fight for credits, and why they sometimes take movies to arbitration in order to get the credit they feel they deserve. Our more detailed explanation of the arbitration process can be found here.