These two stones can look a lot alike when cut into beads. Tiffany stone comes only from the Brush Wellman beryllium mine in the Western deserts of Utah. The mine is not public for collecting and very little of this material is available. It is a soft to hard Opalized stone composed of predominantly Opalized fluorite (blues, purples and whites), often with many other minerals such as Agate, Dolomite, Rhodonite, Manganese oxide, Beryllium and others. It often has a "crackled" appearance and is considered one of the most scarce, beautiful and unusual stones in the world.
Morado opal is a purple and white opal with minor amounts of silica from central Mexico. Morado means purple in Spanish. It is composed mainly of silica with minor amounts of fluorite. The fluorite gives some specimens a blue to violet fluorescence under a shortwave ultraviolet lamp. The purple color in the stone is also attributed to the fluorite.
Both stones having flourite which is where the purple color comes from, the Tiffany Stones can have many other hues found including pink, ruge, yellow and cream. While you will find a lot of freeform cabochons on the market, both stones are not commonly found cut into beads, especially the Tiffany Stone.