First off, neither are going to the max.
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35. Does having Bird rights mean that free agents can be signed and not count against the cap?
With very few exceptions, all salaries are included in team salary.
The Bird exception simply enables a team to exceed the cap to sign certain players. The player's new salary applies toward the team salary just like the salaries of the team's other players. So if a team is over the cap and uses the Bird exception to re-sign its own free agent, it will end up farther over the cap.
http://www.cbafaq.com/salarycap.htm#Q35