Main Difference
The main difference between Theseus and Perseus is that the Theseus is a legendary king of Athens and Perseus is a legendary Greek hero and founder of Mycenae
Theseus
Theseus (UK: , US: ; Greek: Θησεύς [tʰɛːsěu̯s]) was the mythical king and founder-hero of Athens. Like Perseus, Cadmus, or Heracles, Theseus battled and overcame foes that were identified with an archaic religious and social order. His role in history has been called “a major cultural transition, like the making of the new Olympia by Hercules”.Theseus was a founding hero for the Athenians in the same way that Heracles was the founding hero for the Dorians. The Athenians regarded Theseus as a great reformer; his name comes from the same root as θεσμός (thesmos), Greek for “rule” or “precept”. The myths surrounding Theseus—his journeys, exploits, and friends—have provided material for fiction throughout the ages.
Theseus was responsible for the synoikismos (‘dwelling together’)—the political unification of Attica under Athens—represented emblematically in his journey of labours, subduing ogres and monstrous beasts. Because he was the unifying king, Theseus built and occupied a palace on the fortress of the Acropolis that may have been similar to the palace that was excavated in Mycenae. Pausanias reports that after the synoikismos, Theseus established a cult of Aphrodite Pandemos (‘Aphrodite of all the People’) and Peitho on the southern slope of the Acropolis.
Plutarch’s Life of Theseus (a literalistic biography) makes use of varying accounts of the death of the Minotaur, Theseus’ escape, and the love of Ariadne for Theseus. Plutarch’s sources, not all of whose texts have survived independently, included Pherecydes (mid-fifth century BCE), Demon (c. 400 BCE), Philochorus, and Cleidemus (both fourth century BCE). As the subject of myth, the existence of Theseus as a real person has not been proven, but scholars believe that he may have been alive during the Late Bronze Age possibly as a king in the 8th or 9th century BCE.
Perseus
In Greek mythology, Perseus (; Greek: Περσεύς) is the legendary founder of Mycenae and of the Perseid dynasty. He was, alongside Cadmus and Bellerophon, the greatest Greek hero and slayer of monsters before the days of Heracles. He beheaded the Gorgon Medusa for Polydectes and saved Andromeda from the sea monster Cetus. He was the son of Zeus and the mortal Danaë, as well as the half-brother and great-grandfather of Heracles.