Style

Classic:  The original form of cross-country skiing where the skis follow tracks in the snow.  Sometimes referred to as diagonal stride or stride-and-glide.

Herringbone: A method for classic skiing up steep hills.  Skis are in a 'V' shape, and there is no glide phase.  

Double Pole: A classic skiing technique where only the upper body is used for power.

Skate:  A newer form of cross-country skiing that resembles ice skating.  Also known as freestyle.

V1: A skate technique where used primarily for going uphill where the poles are planted on only only one side of the skating action.

V2: A skate technique where a double poling action accompanies every leg push.

Skis

Classic Skis:  Typically longer than skate skis, the middle portion is covered with kick wax.

Fish Scale Skis:  Waxless skis for classic touring.

Skin Skis: A newer version of waxless classic skis.

Skate Skis:  Smooth skis with only glide wax for skate sking.

Wax

Glide Wax: Wax applied for speed to the gliding portions of the ski.  Usually ironed in or sprayed on.

Paraffin Wax: A form of glide wax.

Fluoro Wax: Expensive, fast glide wax.  Currently banned from competitive racing.

Kick Wax: Wax applied to grip the snow during the kick phase of classic skiing.

Klister: 

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