Please explain to me what is the different between acrylic, gel, silk, crystal nails and other nail services. I often hear manicurist say that crystal nails are better than the rest of the products. It seems like acrylic would damage my nails. Is it true?

None of these services should damage your nails. Acrylics (or any enhancement for that matter) do not damage nails, poorly trained technicians damage nails.

Gel Manicure - Gel applied to the natural nail, a very thin application that will soak off with acetone in usually under 10 minutes. This is meant to be a replacement for nail polish application during a regular manicure. Dries under a UV lamp.

Acrylic is a liquid & powder mixed, applied with a brush and will harden (cure) with no lamps in 2 minutes or less. Color and glitter acrylic powders can be used for all kinds of dazzling effects and art.

Gel is, in basic terms, pre mixed acrylic that almost always needs to be cured under a UV lamp, Acrylic usually has an odor while gels are odorless, but both have vapors and need to be ventilated. Color and glitter gels can be used for all kinds of dazzling effects and art. When color gel is used, it is sometimes called a Gel Manicure. See Tell me about Gel Manicures for more information.

Fiberglass or Silk (and sometimes linen) is applied with resin (glue) and sometimes glue & acrylic powder. 

Crystal nails is any enhancement done with CLEAR acrylic, gel or resin. 

Glue & Powder is just that.. nail glue is brushed onto the nails and acrylic powder should be sprinkled onto the glue - not dipped, but sprinkled. The application air dries or a accelerant can be sprayed or brushed on to make the glue dry faster.