As far as I know, there is no universally accepted terminology for cubing, and even if there is, few people know it. So confusion is common and rampant. For this tutorial we will use the following exact conventions.
Corner - a physical plastic corner piece. Has 3 stickers.
Edge - a physical plastic edge piece. Has 2 stickers.
Piece - a corner or an edge.
Sticker - a colored sticker. Those that are nine on each side. You know what I mean. I used to call them "facelet" on the site 1996-2006. I can't explain why.
Side - one of the 6 sides of the cube.
Layer - the cube consists of three layers (top/middle/bottom). This is a 3-dimensional concept, as opposed to "side" which is 2-dimensional. The "green layer" is the one with the green center, regardless of how many green stickers are on it otherwise.
Twist, twisted - how a piece is oriented. A corner can be twisted in 3 different ways, an edge in 2.
Turn, turning - the physical act of rotating a side.
Position (noun) - a place in the cube, relative to the centers The red-white position is the edge position between the red and white cneters. Positions don't move, pieces move by occupying different positions. For example the red-white edge can be in any of the 12 edge positions, and it can be in the correct (red-white) position but wrongly twisted.
Position (verb) - to put a piece in its correct position.
Cube position - an, uh..., position of the whole cube. It's entire state.
Move sequence -
a useful sequence of turns.
I have given names to those move sequences (Niklas, Sune and Allan) that you need to learn by heart. It becomes impossible to talk about them otherwise. There is no particular logic to the names, I just picked them for fun. I believe that is my privilege as inventor of the method.