The second-largest species, the big-mouthed basking shark, was unlikely to bump into its cousin as it prefers colder waters and was cruising from Cook Strait south.
Only about five shark types - of four dozen species - are considered dangerous to people.
There have been 44 shark attacks in New Zealand, a quarter of them fatal, since the 1850s. By contrast, 57 people drowned at sea or in tidal waters last year.
Great whites, bronze whalers and mako attacked people and Te Ara, The Encyclopedia of New Zealand, says blue sharks and threshers are potentially dangerous.
The most common big sharks in the north are hammerheads and bronze whalers. There are nine hammerhead species globally but only the smooth hammerhead in New Zealand. Youngsters up to 1.5m long stay here all year.
"They live mostly in harbours, shallow estuaries and coastal waters," Francis said. Adults are thought to visit the tropical South Pacific, including Tonga.
A "bronzie" up to 3m long spooked a swimmer at Papamoa on Tuesday.
North Islanders are most likely to spot bronze whalers but the sharks travel as far south as the Marlborough Sounds in summer.
Down south, great whites and seven-gill sharks are the most prevalent big sharks.
Adult great whites are concentrated near seal colonies in Stewart Island, Otago and the Chathams. Juveniles under 2m are more common in the north, especially around the Manukau and Kaipara Harbours.
Almost all great whites over 2m leave local waters in winter. Individuals tagged in Stewart Island and the Chathams since 2005 have checked in at tropical destinations including Queensland, Fiji and New Caledonia. Tagged individuals have never crossed the equator.
Makos up to 2m are now in most coastal waters but are more common in the North Island. Blue sharks have also been seen off Gisborne by staff at local dive firm Dive Tatapouri.
A shark relative, the stingray, came to attention this week with some stabbings. Warmer coastal waters and shellfish are attracting the animals. Swimmers can avoid stingray tails by splashing about to scare the rays.
"Stingrays are docile," Francis said. "They'll only lash out with their barb if they feel endangered."
New Zealand's deep seas host 40 to 50 shark species, including the alien-looking goblin shark.
"They're living in areas where there's virtually no light so they use other senses like sound, pressure waves and electromagnetic field," Francis said.
The shovel-nosed dogfish and the seal shark are the most common deep-water species.
Among small sharks, the rig, or spotted dogfish, is common in Auckland, easily seen in the Hauraki Gulf, Manukau and Waitemata harbours.
"Rig will come into shallow water and give birth to their young. In the winter they disappear off the edge of the continental shelf into deep water," Francis said.
Like school shark, rig is often sold as lemonfish. By sheer numbers, the spiny dogfish is the most common shark but it is unlikely to spark panic or interest headline writers - it does turn up from time to time in your fish'n'chips.
