A lot of the "differences" can be found in the "options".

Traditional kilts won't have pockets, for example, that's what a sporran is for!
A traditional kilt will be made out of wool (13oz +), have leather straps and buckles to close it (no velcro for the trads) and pleats only in the back.

Now, the confusing issues arise with semi-traditional kilts. These can be cut to ride lower on the hips (as has been stated), made from poly blends, acrylic, etc, but retain the overall look of a kilt. You can even sneak pockets into a semi-trad if you're clever.

Some examples:

Trad: 8 yard hand-sewn (or even machine stitched) 16 oz wool kilt, done in a tartan (not always), knife pleated to the sett (or stripe, or maybe even box pleated but this is open for debate), and is donned with two or sometimes three leather straps and buckles. These kilts will have a liner, and will be made to measure.

Semi-traditional: SWK (or insert your favorite semi-trad kilt brand here) 4-5 yard acrylic kilt, done in a tartan, knife pleated to the sett. No pockets, the fabric is nice and heavy, but there is less of it. These are usually more "off the rack" kilts, that are made to fit a certain natural waist size with the rest of the kilt measurements being extrapolated from that one measurement.

Non-traditional or contemporary: This is pretty much everything else. UK's, kilts with pockets, kilts in denim, etc. Anything goes. Well, almost anything. With a departure from the traditional cut/fabric of the kilt comes freedom for the garment manufacturer/designer to explore more ideas for the manliest of unbifurcated garments.

These are not static boundaries, and this was by NO means a complete list, just a starter guide. I hope that it helps.