Are the 14 Bravais lattices really distinct? I have learned that there are 14 distinct Bravais lattices in 3D and any other thought lattice form could be reduced to or expressed in one of these 14 forms. But the primitive unit cell for f.c.c lattice is seen to be a special case of trigonal (rhombohedral) lattice (with angles equal to 60 deg). A similar case is true for b.c.c lattice.
So, is f.c.c really distinct while it could be expressed as a special case of trigonal lattice?
 A: The Bravais lattices are not defined by interaxial angles and primitive vector lengths, they are defined by the group under which they are invariant. The group under which a lattice is invariant puts conditions on the interaxial angles and primitive vectors, not the other way around-see Space Groups for Solid State Scientists for an example of how these calculations work.
For example, even though the simple cubic lattice is a special case of the trigonal lattice with $\alpha = \beta = \gamma = \pi/2$, it is considered distinct because the group under which the simple cubic lattice is invariant has more elements than the trigonal lattice. In particular, the trigonal lattice is invariant under rotation about a body diagonal of $2\pi/3$--as is the simple cubic lattice. But the cubic lattice is invariant under rotations about any lattice vector by $2\pi/4$, which the trigonal lattice is not.
You are correct that if classification of Bravais lattices was performed using interaxial angles and primitive vector lengths, there would be no "natural" way to distinguish trigonal from simple cubic.
