Tanzania is a union, not a mainland with a beach attached. The Serengeti and Ngorongoro are the dry-season reason people book a year ahead. Kilimanjaro is a walk you train for. Zanzibar is the same country: Stone Town alleys, clove and cinnamon farms, and a ferry from Dar es Salaam that is a morning on the water if the sea behaves.
Pay park fees and many safari quotes in US dollars; buy street food, dala-dala rides and market fruit in Tanzanian shillings. ATMs exist in Arusha, Dar and Stone Town and then become a rumour. Zanzibar is not a separate SIM country — it is Tanzania — but the spice island still runs on its own clock, dress code and ferry timetable.
Do not try to do the northern circuit, the mountain and a full Zanzibar week in ten days. Pick a safari block or a climb, then take the Azam-style ferry or a short flight to the island and slow down. Eat pilau, mchuzi and a Zanzibar mix; tip the crew and the guide because that is how this industry actually works.