Well, the photo won't come up for me, so I can't be sure, but if the tug loop itself can be 'snugged down' around the shaft, so that it actually 'grips' the shaft, then that is generally described as a French tug(there is a similar type, common on Lutke harnesses, that is called a 'Tilbury' tug; works the same way-that is, by being able to 'slide'the strap end(the loop being constructed of a continuous strap)through a 'tongueless buckle' of sorts, to tighten around, and 'grip', the shaft, then that shaft end buckles into a strap, with a buckle at each end, that mounts on top of the girth via 'keepers', that it will slide.) Same for both sides of the horse. I really couldn't tell if that's the 'set up' in rabbitsfizz' photo, but my guess is that it IS of that type. I've yet to see an explanation of what, if any, difference there is between a French and a Tilbury tug--my own thought has been that it depends on the origin, and I have presumed that 'Tilbury' was of English origin, but ??? I do know that you ask for 'Tilbury' tugs when ordering from Lutke, if the 'snug down' type is what you want. I have recently read(a reliable source) that this type of tug is proper only for gig type shafts,and gig harness, however(and you don't see that in the miniature horse show ring very often, if at all!) Because Portia recommended that I order Tilbury tugs when I got my first Lutke harness, I did--one thing I found IMMEDIATELY was that they mangled my shaft covers! I believe they are popular for mini horse show harness because they are 'minimalist' in appearance-less bulk even than refined wrap straps--and since open tugs with a holddown strap(as in the picture Leis posted) should absolutely be used with breeching (and tug stops),and(right or wrong?),and, people don't/won't use breeching--the choice becomes Tilbury/French tugs. One needs to be very careful not to exert DOWNWARD pressure when buckling the holddown OR wrapstraps into the overgirth on ANY harness, as this means discomfort(too much pressure on the harness saddle)for the horse. The basic purpose of those is to prevent the shafts of a CART(=, two wheeler)from flying upwards(and the cart tipping over backwards and dumping its driver/passengers!) when mounting/sitting in the cart, but there should NOT be a downward "pull" on the shafts from the holddowns/wrapstraps! The horse is supposed to draw the weight of cart and occupant(s) via the breast collar or neck collar, and the traces--NOT the tugs-with Tilbury/French tugs, one needs to be sure that the traces are of a proper length so that that the horse does not end up 'pulling' with the tugs. I would strongly recommend properly-positioned tug stops with this type of tug.
Margo