2. The player contracted to play until August.
The first one is passive and the second one is active. They have the same meaning. The difference is very small. The first one emphasizes the player and the second one emphasizes the contract.
2. Several computer engineers have been contracted with the finance department.
I wouldn't use "with" in this context but you could say "have contracts with"
(I'm not a teacher)
Student or Learner