Lucy:
Your initial question about the flanging seems to have exploded to many other subjects. I will try to give you answers to whatever I remember from the above thread...
Re. flanged and double flanged concept. This means the same thing, i.e. the valve has a flange at each end. A specifically single flanged valve is generally considered a lug type valve. Lugs are typically tapped to allow the valve to be bolted between the pipe flanges from both ends. I have come on ocassion across a spec that described a single flanged valve as a valve with lug body, but drilled through, not tapped, which functioned as a wafer body, but still allowed simple bolting to a dead end without a redundant downstream flange.
Re. differences between flanged (i.e. double flanged) and a lug or wafer. Here you have to be careful, the laying length i.e. face to face dimension of a flanged valve is significantly wider than of a lug or a wafer valve.
Re. rubber seated, metal seated, Teflon seated, graphite laminates, etc. butterfly valves. These are all very different animals, for different applications, and the costs differ significantly.
Commercial type rubber seated BFV would be the low cost end and a metal seated triple offset valve like the one with the stainless and graphite laminated disc seal you mentioned above, would be on the high end of the price ladder.
However, the applications of these valves can overlap, so your selection should, amongst other, be governed by cost considerations. Generally, rubber seated valves are good for low pressure (250 psi max) service, and low temperature (300 F max) for very vast selection of flow media, depending on what rubber is used.
Teflon lined valves can either be plain zero offset valves same as the rubber seated valves, except these valves are suitable for more corrosive service than rubber seated valves; or they can be double offset or even triple offset hi-performance valves for higher pressure and higher temperature service. Pressure is more or less unlimited, and temperature is limited to somewhere between 400 and 500 F, depending on the fill in the Teflon material.
Metal seated butterfly valves can be either damper type (somebody mentioned) with leakage rate varied usually by the valve size (very difficult to get a small damper to conform to a low leakage rate); or metal seated valves can be double or triple offset type. Double offset metal seated valves are usually used together with Teflon seats and are the so-called common fire safe hi-performance valves. Triple offset metal seated valves are of various construction, but in most cases, use a laminated seal ring, either on the disc or in the body, to seal against very high temperatures and very high pressures. Triple offset metal seated valves are inherently fire safe, and inherently cryogenic (with neck extension). Contrary to what was stated by someone above about class VI leakage rates, reputable manufacturers produce triple offset metal seated valves to perfect bubble tight seal. Triple offset valves are normally not used in corrosive applications, and would be an overkill in a plain water application. Typically, high temperature service like steam would be the common use for triple offset BFVs.
Well, I hope this is enough for now...
Good Luck...