Shor (quantum polynomial), Number Field Sieve (subexponential), Pollard rho (square root) all have both factoring and discrete logarithm over $\mathbb F_p^*$ variants.

What are the subexponential techniques that only applies to

balanced semiprime integer factoring but not to discrete logarithm over

some knowncryptographically important structures including $\mathbb F_p^*$ and Elliptic Curve Discrete Logarithm?balanced semiprime integer factoring but not to discrete logarithm over

all knowncryptographically important structures including $\mathbb F_p^*$ and Elliptic Curve Discrete Logarithm?discrete logarithm over

some knowncryptographically important structure including $\mathbb F_p^*$ but not to balanced semiprime integer factoring?

Please provide references appropriately.