As far I understand, 1 distinctive feature of such algorithm is it fully works in subgroups/suborders.
All other index calculus algorithms can do this only for the linear algebra phase and thus their complexity is determined by the field size. Thus when the discrete logarithm only lies under a large prime factor, this makes a situation making Pollard’s rho faster than modern index calculus methods if the field is too large.
Of course, the factorization part of Adleman can be done using more modern methods…