The only difference is that she will periodically advise the carrier on the status of the case and report on any significant matters. Any discussion between your senior management employees and the attorney are covered by the attorney-client privilege, just as if you had selected her and were paying for her services. That relationship is significant, particularly if the carrier raises coverage issues. Under ethical rules, the attorney isn't allowed to pass on to the carrier facts you provide her that may negate insurance coverage. Any significant dispute arising between you and the carrier is usually addressed by other attorneys.
Most insurance contracts allow the insurance carrier to select the defense counsel.
So while you may have counsel that you use for business and litigation purposes, the carrier may not select him to handle your defense. You could argue that the attorney who regularly handles your business is best suited to defend you in litigation, particularly since he is already familiar with you and your business. But your carrier may be more comfortable working with attorneys it already knows. If you want to ensure that your regular attorney is assigned to handle the litigation, you should discuss your wishes with your agent as well as the adjuster who is supervising the litigation. A number of carriers have instituted guidelines in an effort to control the cost of litigation.