In a CGL, defense is a supplementary payment that does not reduce the limit of insurance. The duty to defend ends only when the limit is used up by paying judgments, settlements or medical expenses.
Professional liability forms commonly put defense costs inside the limit, so every defense dollar erodes what is left to pay the claim. Example: a contractor's CGL and a lawyer's malpractice policy each have a $1,000,000 limit, and each insurer spends $200,000 on defense. The CGL still has $1,000,000 for a settlement; the malpractice policy has $800,000.
Many professional forms also give the insured a say in settlement, often called a consent to settle provision, because a settlement can hurt a professional's reputation. A CGL does not give the insured that say. Professional forms vary, so always read the specific policy.
California independent counsel: Civil Code §2860 applies to any policy that imposes a duty to defend, so it matters for both CGL and professional policies. Under §2860(b), a conflict of interest may exist when the insurer reserves its rights on an issue whose outcome can be controlled by the counsel it retained. In that situation the insured may be entitled to independent counsel paid for by the insurer. The same subdivision says no conflict exists as to allegations for which the insurer denies coverage, as to punitive damage allegations, or solely because the suit asks for more than the limits.