Parallel, counterpart, analogue, correlate are comparable when they denote a person or thing that corresponds in essentials to another person or thing, or closely resembles the latter in the points under consideration.
Parallel is especially appropriate when the two things compared are so like each other that their lack of divergence suggests two parallel lines; the term is often used in negative expressions.
Sometimes, especially when actual comparison is implied, the word suggests that the two things follow a similar course, order, or line of development.
Counterpart often suggests a complementary and sometimes an obverse relationship.
More commonly, however, the word implies a duplication, especially in another sphere, or age, or language.
Analogue usually implies a more remote likeness than the preceding words and suggests comparison with something familiar and tangible for the sake of clarifying an explanation or enforcing an argument. Like counterpart, it often involves reference to something in another sphere, or order, or genus.
Correlate retains its primary implication of correspondence, but does not retain that of a complementary relationship. A thing which is a correlate of another is what corresponds to it from another point of view or in a different order of viewing.