It is difficult to distinguish the two minerals by ordinary means. Tennantite is generally darker, has a redder streak and a translucent red color that can be seen in thin splinters when they are held up to a strong light. Tetrahedrite is by far the more common of the two. Tetrahedrite is named for the common form, the tetrahedron, that both tennatite and tetrahedrite form.
The tetrahedron is an interesting isometric crystal form. It is obvious where the four three fold axes of the isometric system belong, as each one exits out of the crystal through each of the four identical "pyramidal" peaks. However the four fold axes are evidently missing. They aren't, they are just four fold rotoinversion axes. A four fold rotoinversion axis takes a face, rotates it 90 degrees (one fourth of a rotation) and then inverts it (up to down & right to left) through the crystal to the other side. Then it rotates it again 90 degrees and inverts it again through the crystal. Another rotoinversion operation and finally another (four in all) and the face is back, exactly where it started. The result is two faces on the "top" and two on the "bottom" of the crystal but in perpendicular orientation. The tetrahedral faces of tennantite are in many instances modified by other crystal forms giving the crystals multiple facets while still retaining the overall tetrahedral shape.
Tennantite is in an informal group of minerals called the "fahlerz" or "fahlores" group. The group is named for an old german miners word meaning "pale ore". Most members of the tetrahedrite group belong to this informal group.
Although rarer than its cousin, tennantite forms nice crystals and can be a handsome specimen. Often tennantite will contain a certain percentage of silver and be used as a minor ore. Collectors usually crave nice specimens of verified tennantite.