Is there any relationship between Hare Krishnas and Hindus, or do these belong to two entirely different religions?
Hare Krishnas are Hindus as they worship Lord Krishna. Krishna is the 8th incarnation of Lord Vishnu(among the major incarnations).
Hare Krishnas chant the Mahamantra
"Hare Krishna Hare Krishna Krishna Krishna Hare Hare
Hare Rama Hare Rama Rama Rama Hare Hare:"
Which is from Kali-Santarana Upanishad. Upanishad are part of Vedas. So they follow Vedic religion.
But Hare Krishnas are not the only Hindus. Hare Krishnas believe Lord Krishna to be supreme, Shaivites believe Lord Shiva to be Supreme, Vaisnavas believe Lord Vishnu to be Supreme, Shaktas believe Devi to be Supreme, Ganapatyas believe Lord Ganesh to be Supreme, Suryaties believe Lord Surya (Sun God) to be Supreme, Shankhyas don't believe in God (Prakirti and Purush do all for them) and so on.... But they all are considered Hindus (as they all accept authority of Vedas).
All Hare Krishnas can be considered Hindus, but all Hindus aren't Hare Krishnas.