Disclaimer: These are my definitions that I am currently using, they are not the definitions that everyone uses and they are not the definitions as used in the Manual. The Manual was written almost ten years ago, we've evolved and continue to evolve. If someone is using a definition of thier own you'll have to ask them to explain it. Good luck.

General Terms

The Cast, the act of delivering the fly, from the moment the flycaster first begins the cast to the moment the fly lands

The Back Cast, the act of delivering the fly backwards

The Forward Cast, the act of delivering the fly forwards

The Essentials

Power
Drift: [powerless] rod repositioning, with negligible effect on the flyline
Sweep: [semi-powered] rod motion with sufficient energy to relocate line by pulling it into place
Effective/Power Stroke: [powered] rod motion in which the rod tip accelerates the line with sufficient energy to form a casting loop.

Structure
Complete Stroke/Stroke, the complete form of body and rod from when it first moves in the direction of the cast to either when the structure of the cast changes direction or the cast is complete
Effective Tip Travel, the path the tip follows while it accelerates the line
Effective Casting Angle/Rod Arc, the angle the rod rotates through while it accelerates the line with sufficient energy to form a casting loop.

Drag, primarily rod translation during the Effective Stroke.
Slide, drift in the direction of the subsequent effective casting arc, occuring while the hauling hand is returning to meet the rod hand.

That's the basic model. Using this structure;

Creep, subconscious rod drift.
Straight Line Path (SLP), an imaginary path of the rod tip, the closer Tip Travel follows this line the narrower the loop.
Rod Straight Position (RSP), the point when the rod passes straight position, commonly argued as the point of loop formation - this is not always the case but RSP is a useful term.
Loop Straight Position (LSP), the point when the loop straightens
Counterflex, The rebending of the rod as passes RSP forming the bottom of the loop.

Butt Rotation, The rotation of the butt during the Effective Rod Arc.
Follow Through, Drift in the direction of the Effective Stroke occuring immediately after RSP

Haul, a continuous pull of the flyline with the non-casting hand.
Single Haul, one haul
Double Haul, two back-to-back hauls; one on the backcast, the other on the forward cast
Check Haul/Tug, A [short] haul occuring just prior to final unrolling of the loop
Triple Haul, [minor usage] a double haul followed by a check haul

More will follow as these are refined.

Cheers,
Paul

Amended March 2009