That's not how my (London) tailors use the term. They use it to describe lining as in the post below. It's because the lining looks like the canopy on an old car.http://thesavilerowtailor.co.uk/2011/06/buggy-half-lined-jackets/
I don't think you should take 'the majority here' as being representative or a good model if you are just starting out on the bespoke journey. At least your first 6 (imo) suits should be made in conservative 'basic' cloths supplied by your tailor. Supplying your own cloth (known as CMT on Savile Row, or 'cut make and trim') should only be considered/necessary once you have the foundations of a decent suit collection and have developed a good relationship with your tailor.