Torsion angle symbol
It is a habit to assign greek letters (most often lowercase) to angles. In case of "normal" angles, it's mostly $\alpha, \beta, \gamma$, whereas for dihedrals some higher letters, as you mentioned, $\phi, \psi, \omega$. As noted in comments, whatever you use, clearly state what you mean.

The difference between dihedral and torsional angle is more conceptual, then formal. In torsion you discuss rotation around a bond, dihedral is general angle of two planes, as mentioned in the $\ce{CH_4}$ example. The formal expression for both of them is the same, indeed.

To be noted, there are some well known widely used dihedral angles, where you should stick to the common notation. The most prominent example is the protein backbone arrangement, see Ramachandran plot. In this case you should not invent your own notation.