The significance of Type A and Type B, boiled down:
If a Type A free agent signs with another team, the team that lost him — assuming it offered arbitration — gets at least a supplemental first-round pick next June. In many cases, they also get the first round pick of the signing team. (It gets complicated; it depends on how good the signing team was and, in some cases, how many Type A free agents it has signed.)
If a Type B free agent signs with another team, the team that lost him — again assuming it offered arbitration — gets a supplemental first round pick.
Orlando Cabrera is a Type A free agent, but his contract specifically prohibits the Twins from offering arbitration.