島 and 半島: an island and land projecting into water
Compare the land connections of an island and a peninsula, without changing an island into a peninsula merely because a bridge connects it.
Land surrounded by water
島, read しま, means an island surrounded by water. 湖の中に小さな島があります。 says that there is a small island in the lake.
船で島へ渡りました。 says that someone traveled across to the island by boat. 島へ marks the destination, and 船で the means of travel.
Land projecting from a larger land area
半島, read はんとう, means a peninsula projecting into a sea or other body of water. 半島の先に灯台があります。 places a lighthouse toward its tip.
半島の付け根に町があります。 locates a town at the peninsula’s base, where it joins the larger land area. Do not swap the positions given by 先 and 付け根.
A land connection and a bridge
島と本土は橋でつながっています。 says that the island and mainland are connected by a bridge. An artificial connection does not automatically change the translation of 島 to peninsula.
半島を一周しました。 says that someone went around the peninsula. 一周 describes the route taken; it does not say that water completely separates the peninsula from the mainland.
Should 島 be translated as peninsula in 島と本土は橋でつながっています。?
Show the answer and why
No. The sentence explicitly names an island connected to the mainland by a bridge. Distinguish the bridge from a connection formed by the land itself.