Some lens manufacturers have special names for their lens designs/families. Just to name a few:
What do these mean and do they carry any important information from the buyer's perspective?
The Leitz/Leica designations refer to the maximum aperture rather than the overall lens design.
Like the Carl Zeiss lenses, the Vario prefix means it's a zoom lens.
A lot of lens names are a product of the overlap between the engineering and the marketing sides of the lens design process. The names themselves are created to sound appealing to customers, and many of them are variations on common terms in optical engineering.
In addition, it is common in optical design to use an existing lens as your starting point when creating a new lens. This is because, while there is a lot of science behind lens design, it isn't possible to simply look at the specifications you are trying to achieve, and then calculate the ideal form for a lens. Lens design is partially concrete and mathematical, and partially a creative process that depends on the lens designers experience and intuition. This means that it is much more effective to take an existing design that has similar properties to the lens you are trying to design, and make modifications to it, rather than start from scratch every time.
The result is that you have lens families which are all descendants of a few classic forms that get used over and over again. A complicated zoom lens may start the design process as a Double Gauss lens, with 6 elements in 2 groups, symmetrical about the aperture stop; by the time the design process is done, the lens may have over a dozen elements in a handful of groups, a few of which may move, and the aperture stop may be in a completely different location. An experienced lens designer would be able to look at that design and immediately see that it was probably produced from a Double Gauss.
When this happens with patented commercial lenses, like the Tessar for example, it is common for the resulting lens to be sold under the Tessar family name. Because it shares a lot of optical design traits, but also because it gives consumers an idea of what the lens is good at doing. Most lenses in a family will have similar characteristics and uses, in very general terms. You wouldn't start the design of a new wide-angle lens with a design form used for very long telephoto lenses; you would chose a similar lens to the one you are trying to produce, so the resulting families tend to be grouped loosely by their intended application.
Of course, because this is tied to marketing, there will be exceptions. Lens designers don't name lenses, and if some marketing guy things that a lens will sell better if he gives it a particular name, I doubt anybody will care how much this irritates the lens designer.
Carl Zeiss lens families are in fact different lens designs (as in combination of optical elements). You can read about them at Wikipedia:
To answer the second part of your question, NO you should not care about the family name in itself.
When choosing a lens, look at the specifications (focal-length, maximum aperture, magnification, etc) to suit your needs.
Then look at the MTF charts, sample images (full-size only) and reviews to know about quality. A goof place to look is SLRGear which has excellent lens tests which show softness, vignetting at almost every combination of aperture and focal-length.
Do you really care if that awesome MFT comes from a Double-Helix Inverted Ultra-Hyper-Glass design or from a Triple-Phase Super-Dupper-Luminomatic design?
Hint: None of these have been invented yet and the future manufacturers will both patent this as the best lens design ever :)
