A Gel Manicure and a Shellac Manicure are essentially the same thing: long-lasting polishes cured under a LED or UV lamp. The difference is that a "gel manicure" is the generic term for nails done under a curing lamp, while Shellac is a brand of gel product patented by the company Creative Nail Design (CND).
"Shellac" is a hybrid, of a mixture of nail polish and gel. The product can be applied similarly to nail polish on your natural nails, layered thinning for best results, without the need for sculpting or filing down, unlike acrylics, hard gel nor SNS.
Though a little thicker in constantly, it cannot be used to extend the natural nails. However, the gel component in the "Shellac" will add strength and durability to the nail and in the long term, it should not cause damage your natural nails as much as a traditional nail enhancement, if the application and removal process is done correctly by a professional nail technician.
A professionally done Shellac manicure should last up to two weeks, with high gloss density, and removed as soon as there is any signs of lifting, cracks or breakage, so as not to destroy the quality of your natural nail bed, which is a very important step to keep your nails strong and healthy in a long run.