No. They are not the same. It is almost always better to have an individual policy rather than a group policy. For these reasons, you should purchase an individual policy over a group policy:
What’s the Difference Between Individual and Group Disability?
A major difference between individual and group policies is that individual policies are underwritten with respect to the individual purchasing insurance coverage, while group policies are not individually underwritten. Instead, group policies are issued by disability insurance companies based on certain underwriting assumptions related to the general health of a group of people.
Individual policies are typically bought and paid for by the insured, separate and apart from an employer. Group coverage, on the other hand, is usually offered by an employer or union, and the premiums are paid (in whole or in part) by the employer. There may be circumstances where an employer will purchase and pay the premiums for an individual policy on behalf of an employee. Conversely, an individual may personally obtain group LTD coverage unrelated to his or her employment by joining a group that has group coverage available for its members. The monthly benefits are tax-free if you pay the insurance premiums yourself. If the premiums are paid by a business employer, you may have to pay tax on the benefits.
Moreover, if the insurance company does not pay a claim, your legal rights with an individual policy are very different from your legal rights with a group policy. If the insurance coverage is under a group policy provided by the insured’s employer, the policy is likely governed by ERISA. If the policy is governed by ERISA, then certain state laws that offer consumers protection and remedies for relief are “preempted” by ERISA regulations. In short, if the LTD plan is governed by ERISA, the disability insurance company has no exposure to bad faith damages and thus has no real incentive to pay the claim.