"Barely there" vs "Single tier"
Here are some photos of my barely there veils - they have a slight cascade effect at the sides, in order to be totally sheer at the comb:
Here's a photo of one of my classic single tier veils, which clearly shows the shape of this style - this one has a lace edge. I've used this photo because the lace edge clearly defines the edge of the veil, so it's easier to see how it's cut (ie with straight sides and a curved bottom edge):
The barely there styles have no gathering at all, so they're very sheer and lay flat against the hair, whereas the classic single tier styles are gathered, so they're slightly less sheer and they have a little bit of "lift" where the comb is pushed into the hair.
Please do ask if you need any further help!