here is the thing. The common term is snailshell due to the expansion of the port giving specific acoustical properties that have direct control over the response curve from its pure physical porperties resembling much like a snail shell with obvious differences. Unlike a standard ported design, that relies on compression chamber and port length coupling for resonance control, the so called, "snailshell" inherits properties much like a standard horn enclosure, whereas the efficiency and coupling of the driver/box combination creates higher output as mentioned above. There is a lot to understand about a properly designed enclosure, whether the simplest form or complex to the point of 8th order designs, but in essence as questioned, yes they do give greater output generally using the same applied power as a lower efficient design, IF built and designed properly. But that is not what their main purpose is.....it is mainly geared towards the use of lower amplified sources to achieve equal output, not greater output, though this is an acoustical effect of such enclosure.
I have not heard it called a snailshell in years, but can be referred to as a tapered enclosure with or without compression chamber, either normal taper or reverse.
The actual understanding of the design of these enclosures is complex. And giving a general idea of how they work is not plausible in a single text. But can be learned over time. Just figured I could chime in to help a little....hope it did.
