The Phillabeg or "Little Kilt" is the modern version.

This is the kilt you see on members of Pipe Bands.

I'm as confused as the rest of us when your say "Does this type of kilt have the inner and outer aprons like a 'Standard Kilt.'". It is a standard kilt.

If what you are trying to describe is the kilt that you see worn by Pipe Bands then the definative work on how to make one is "The Art of Kiltmaking" By our own Barb Tewksbury. This book is available at your local library but I suggest you check www.celticdragonpress.com and buy your own copy. Not just well worth the money, this book is a 'must have' for anyone thinking about making their own kilt.