Regular manicures – they will moisturize your cuticles, tidy them up, cut and file your nails, and apply regular nail polish (base coat, color, top coat). How long the polish will last depends, but for me, it’s like, a day. For others, it’s more like a week. It can be removed with regular polish remover.
Gel/shellac manicures – same stuff with cuticles/nails, and then apply gel polish – it is painted on like regular, but they set each layer with UV light. It lasts for two weeks or more – typically you want it removed because it grows out rather than because it chips. It doesn’t hurt your nails in and of itself, but if you try to peel it off, it will pull off a layer of nail. If you go in and get it removed in the salon, you’ll be fine. I HIGHLY recommend this option. It’s the only reason I now have healthy nails; I used to have thin nails that I always bit, but after getting regular gel manis for a few months, they are now gorgeous and I don’t need the gels to protect them. The gels didn’t damage my nails (always had them professionally removed) and now my nails are stronger because they were safe under the gels. It is a bit thicker than natural nails, so they won’t break as easily. Gel/shellac manis look gorgeous; the polish stays glossy and don’t scratch or chip even when abused, unlike regular polish.
Acrylic/’gel nails’ – they deal with cuticles etc, and then grind down your nails, removing the top layers so that there is a rough texture for the fake nail paste to attach to. They then put on tips that make your nails longer, and then apply a paste that sets into a thick ‘nail’. Like gel manicures/shellac, they last for 2-3 weeks, and the issue is them growing out rather than them chipping. They have to be removed in the salon – if you pull them off, you will remove even more layers of the nail. This is what you would do if your nails are super short and you want them long, but it will definitely damage your nails no matter what.
Hope that helps!
ETA: Re-read that you want your nails longer than usual. That gives you two options, depending on what you’re willing to do for it. If you start getting gel manicures now, you can keep them protected so they will be able to grow longer than you naturally can do (as I said, slightly thicker so they won’t break as easily, you can’t bite them, etc) – more of a long-term fix. If you just want a fast fix to have longer nails than you normally do and are okay with them being weak for awhile after the wedding, just do fake/gel nails for the wedding; they will put tips on and you can have them do them whatever length you choose – this will give you a great one-day fix.