The Canadian case is inherited from the British who, in 1621, granted Sir William Alexander all islands within 6 leagues of the coast of "Nova Scotia" to be part of his patrimony. New Brunswick was later hived off from Nova Scotia to become its own province. They can also claim squatters' rights because in 1832 they built a lighthouse and cluster of service buildings that show up as red and white dots on the satellite view [L]. The island is right in the middle of the seaway to St. John NB and the other ports and harbours up the Bay of Fundy, so a lighthouse had clear utility. The lighthouse has been rebuilt and refurbished since 1832 but more or less continuously occupied by Canucks ever since: de facto they own it.
The American case stems from Article 2 of the Treaty of Paris which wrapped up the war of 1812 between UK and USA. That says that any island less that 20 leagues off-shore and South of the St. Croix river is part of the United States of America. The St Croix runs between Calais, Maine and St. Stephen, New Brunswick and I crossed it there in 1981 towards the end of a big road-trip getting data for my PhD. Machias Seal Island is clearly South of the mouth of the river and definitely within 20 leagues of the coast of Maine, so I think de jure the Yankees have it.
At the moment, despite some shape throwing by Prime Minister Trudeau and President Trump. Canada and the USA are at peace with a helluva lot of traffic - both goods and people - across the border every day. Nobody cares enough about the lobsters [which are getting scythed by fishermen from both sides of the border] to start a war and both sides have refused arbitration by the International Court of Justice in The Hague. But if oil is discovered under the sea in what they call the Grey Zone surrounding Machias Seal Island, then we can expect a bit of gun-boat diplomacy. The Atlantic has put together a NatGeog-like documentary about the affair. And/or A life in the day of a lighthouse keeper.
A whole archipelago of other Blobby islands.