"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:
Below is 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, giving a minimal, transparent look, 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, giving a slightly more full and dramatic effect.
Please do ask if you need any further help!