Hostel and hotel are literally the same word — one is the medieval borrowing and the other the modern one, split apart by centuries of French pronunciation changes.
An establishment providing inexpensive lodging, typically for travelers, students, or young people, often with shared rooms and facilities.
From Old French hostel (lodging, inn), from Medieval Latin hospitale (inn, large house), from Latin hospitalis (of or pertaining to a guest), from hospes (host, guest). The word is a doublet of hotel — both derive from the same Latin source but entered English at different times and with different meanings. Key roots: *gʰóstis (Proto-Indo-European: "stranger
Hostel and hotel are the same word — both descend from Old French hostel (lodging, inn). Hotel is simply the modern French form, borrowed into English in the 18th century after French dropped the s (which is preserved as a circumflex accent in hôtel). The medieval English hostel fell out of common use but was revived in the early 20th century when the youth hostel movement began in Germany in 1909, when schoolteacher Richard Schirrmann started converting