My employer offers me LTD coverage as a fringe benefit cheaper than I can buy it on my own. Is the group coverage the same as if I bought my own individual disability policy?

No. They are not the same. It is almost always better to have an individual policy over a group policy. First of all, 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 are very different with an individual policy than with a group policy. In short, your legal rights are much more favorable with an individual policy than with a group policy. For these reasons, you should purchase an individual policy over a group policy.